Chapter-13 exponents and power

Explanation:

Given: Base=2 and power 6

2 is equivalent to multiplying the number 2 by itself 6 times So, this can be written as:

64

Explanation:

Given: Base = 9 and power 3

9' is equivalent to multiplying the number 2 by itself 6 times So, this can be written as:

=9x9x9

=64

Hence, 99 x9x9-27

Explanation:

Given: Base 11 and power = 2

11 is equivalent to multiplying the number 2 by itself 6 times

So, this can be written as :

= 11 x 11

= 121

Hence, 11 x 11 =121

Explanation:

Given: Base = 5 and power = 4

5 is equivalent to multiplying the number 2 by itself 6 times

So, this can be written as

=625

Hence, 5-5 x 5 x 5 x5=625:

Explanation:

In exponential form, the number being multiplied (in this case, 6) is the base, and the exponent indicates how many times the base is being multiplied by itself.

So, 6^4 means 6 multiplied by itself four times, which is equal to 1296.

Explanation:

The expression " x 1" represents the multiplication of the variable t by itself, which can be written in exponential form,

 In general, when a variable or number is multiplied by itself in times, it can be expressed as the variable or number raised to the nth power. So, txt is equivalent to which represents t multiplied by itself twice.

Explanation:

The expression "bxbxbx b" represents the multiplication of the variable b by itself four times, which can be written as in exponential form.

In general, when a variable or number is multiplied by itself in times, it can be expressed as the variable or number raised to the math power. So, bxbxbx bis equivalent to which represents b multiplied by itself four times.

Explanation:

The expression "2 x 2 x ax a represents the multiplication of two 2s and two as, which can be simplified before expressing it in exponential form:

2x2xaxa=4

In exponential form, this expression is written as 4 which means the product of 4 and

In other words, 2x2 x axa is equivalent to 4 multiplied by a squared, where a is multiplied by itself twice.

Explanation:

The expression "a xaxaxcxcxcxcxd" represents the multiplication of three as, four c, and oned, which can be simplified before expressing it in exponential form:

axaxaxcxcxcxcx

In exponential form, this expression is written as 'd, which means the product of a cubed, c raised to the fourth power, and d. In other words, a xaxaxcxcxcxcxd is equivalent to a cubed multiplied by cruised to the fourth power, and then multiplied by d.

Explanation:

To express 512 in exponential notation, we need to find the power of 2 that gives 512.

We can start by dividing 512 by 2 repeatedly until we get a quotient of 1

512/2=256

256/2=128

128/2=64

64/2=32

32/2=16

16/2=8

8/2=4

4/2=2

2/2=1

We can see that 512 is equal to 2 multiplied by itself 9 times (2x2x2x2 or 2

Therefore, we can express 512 in exponential notation as:

512=2^6

Explanation:

To express 343 in exponential notation, we need to find the power of 7 that gives 343.

We can start by dividing 343 by 7 repeatedly until we get a quotient of 1.

343/7=49

49/7=7

7/7=1

We can see that 343 is equal to 7 multiplied by itself 3 times (7x7x7), or Therefore, we can express 343 in exponential notation as:

343=7^3

Explanation:

To express 729 in exponential notation, we need to find the power of 3 that gives 729.

We can start by dividing 729 by 3 repeatedly until we get a quotient of 1.

729/3=243

243/3=81

81/3=27

27/3=9

9/3=3 

3/3=1

We can see that 729 is equal to 3 multiplied by itself 6 times (3x3x3x3x3x3), or j

Therefore, we can express 729 in exponential notation as

729=3^6

Explanation:

To express 3125 in exponential notation, we need to find the power of 5 that gives 3125.

We can start by dividing 3125 by 5 repeatedly until we get a quotient of 1.

3125/5=625

625/5=125

125/5=25

25/5=5

We can see that 3125 is equal to 5 multiplied by itself 5 times (5 x 5 x5 x 5 x5), or 5 Therefore, we can express 3125 in exponential notation as:

3125=5^5

Explanation:

To compare we can evaluate them and compare the results.

=3x3x3x3=81

We can see that 3 s greater than 4

In general, when comparing exponential expressions with different bases, we can use the following rule:

if and only if a>c and b>d

In this case, 

have different bases, so we cannot directly compare the bases. However, we can compare the bases indirectly by looking at their prime factorizations.

4=2

3=3

Since 2 is less than 3, we know that 4 is less than 3

Therefore, we can conclude that 3^4 is greater than 4^3

Explanation:

To compare 5^3 and 345, we can evaluate them and compare the results:

5^3=5x5x5=125

3^5=3x3x3x3x3=243

We can see that 3^5 is greater than 5^3.

In general, when comparing exponential expressions with different bases, we can use the following rule:

a^b>c^d if and only if a>c and b>d

In this case, 5^3 and 345 have different bases, so we cannot directly compare the buses. However, we can compare the bases indirectly by looking at their prime factorizations:

3-3^1

Since 5 is greater than 3, we know that 543 is greater than 343. Therefore, we can conclude that 345 is greater than 5^3.

Explanation: 

To compare 2^8 and 8^2, we can evaluate them and compare the results:

248=2x2x2x2x 8^2=8x864 x2x2=256

We can see that 248 is greater than 8^2

rule:

In general, when comparing exponential expressions with different bases, we can use the following

a^b> c^d if and only if a>c and b>d

In this case, 28 and 8^2 have different bases, so we cannot directly compare the buses. However, we can compare the bases indirectly by looking at their prime factorizations:

2=2^1

Since 2 is the same in both expressions, we can compare their exponents. We can see that 8 is greater than 2, so we know that 28 is greater than 2^2. Therefore, we can conclude that 28 is greater than 8^2.

Explanation:

To compare 100^2 and 2^100, we can evaluate them and compare the results:

100^2 = 100 x 100= 10,000

2^100 is a very large number and is difficult to calculate exactly, but we can use logarithms to estimate its value. Using the rule that log_2(xy)=y log_2(x), we can calculate

log 2(2^100) = 100 log_2(2)=100*1=100

So, 25100 is approximately equal to 2 raised to the power of 100, which is a very large number:

2^100 = approx 1.2676506 x 10^30

We can see that 2^100 is greater than 100^2.

In general, when comparing exponential expressions with different bases, we can use the following rule:

a^b> c^d if and only if a>c and b>d

In this case, 2100 and 100/2 have different bases, so we cannot directly compare the bases. However, we can compare the bases indirectly by looking at their prime factorizations:

2=2^1

100=2^2-5^2

Since 2 is less than 5, we know that 2100 is less than 54100. Therefore, we can conclude that 2^100 is greater than 100^2 

Explanation:

To compare 2^10 and 10^2, we can evaluate them and compare the results:

2^10 2x2x2x2 , 10^2= 10 x 10 = 100 ×2×2×2=1,024

We can see that 2410 is greater than 10^2

a^b> c^d if and only if a>c and b>d

In general, when comparing exponential expressions with different bases, we can use the following rule:

In this case. 2^10 and 10^2 have different bases, so we cannot directly compare the bases However, we can compare the bases indirectly by looking at their prime factorizations:

2=2^1

Since 5 is greater than 2, we know that 10^2 is greater than 2^2. Therefore, we can conclude that 210 is greater than 10^2.

Explanation:

To express 648 as a product of powers of its prime factors, we can use prime factorization.

First, we can divide 648 by 2. since it is an even number:

648/2=324

Now, we can divide 324 by 2:

324/2=162

Again, we can divide 162 by 2

162/2=81

81 is a perfect square, and its square root is 9, which is a prime number. So we have

81=9^2

Now, we can write 648 as a product of powers of its prime factors:

648=2^3x3^4x(3^2)^2

Since 9 is equal to 342, we can simplify this expression further

648=2^3 × 3^4 × (3^2)^2

648=2^3 x 3^4 x 3^4

648=2^3x3^8

Therefore, the prime factorization of 648 is 2^3 x 3^8.

=2^3x3^4 

Explanation:

To express 405 as a product of powers of its prime factors, we can use prime factorization

First, we can check if 405 is divisible by 2. Since it is not an even number, we can check if it is divisible by 3:

405/3=135

Now, we can check if 135 is divisible by 3:

135/3=45

Again, we can check if 45 is divisible by 3:

45/3=15

Finally, we can check if 15 is divisible by 3:

15/3=5

5 is a prime number, so we have completed the prime factorization:

405 = 3^4x5

Therefore, the prime factorization of 405 is 34 x 5.

Explanation:

To express 540 as a product of powers of its prime factors, we can use prime factorization

First, we can divide 540 by 2, since it is an even number.

540/2=270

Now, we can divide 270 by 2

270/2=135

Next, we can check if 135 is divisible by 3:

135/3=45

Now, we can check if 45 is divisible by 3:

45/3=15

Finally, we can check if 15 is divisible by 3

15/3=5

5 is a prime number, so we have completed the prime factorization:

540=2^2x3^3x5

Therefore, the prime factorization of 540 is 2^2 x 3^3 x 5.

Explanation:

To express 3600 as a product of powers of its prime factors, we can use prime factorization.

First, we can divide 3600 by 2, since it is an even number:

3600/2=1800

Now, we can divide 1800 by 2

1800/2=900

Again, we can divide 900 by 1

900/2=450

Next, we can check if 450 is divisible by 2:

450/2=225

Now, we can check if 225 is divisible by 3:

225/3 75

Next, we can check if 75 is divisible by 3:

75/3=25

Now, we can check if 25 is divisible by S

25/5=5

5 is a prime number, so we have completed the prime factorization:

3600=2^4 × 3^2 x 5^2

Therefore, the prime factorization of 3600 is 24 x 32 x 5^2

=2^4x3^2x5^2

Explanation:

we can evaluate the exponential expression by multiplying 2 by 10 raised to the power of 3.

10^3 means 10 multiplied by itself 3 times, which is:

10 x 10 x 10 = 1,000

Therefore, 2 x 10^3 is equal to

2x 1,000 = 2,000

So. 2 x 10^3 simplifies to 2,000.

Explanation:

we can evaluate each exponent and multiply the resulting values.

7^2 means 7 multiplied by itself 2 times, which is:

7x7=49

2^2 means 2 multiplied by itself 2 times, which is

2x2=4

Therefore, 7^2 x2^2 is equal to:

49x4 196

So, 7^2 x 2^2 simplifies to 196.

Explanation:

we can evaluate the exponent and multiply the resulting value by 5.

2^3 means 2 multiplied by itself 3 times, which is:

2×2×2=8

Therefore, 2^3 x 5 is equal to

8x5=40

So, 2^3 x 5 simplifies to 40.

Explanation:

we can evaluate the exponent and multiply the resulting value by 3.

4^4 means 4 multiplied by itself 4 times, which is:

Therefore, 3 x 4^4 is equal to

3x256-768

So, 3 x 4^4 simplifies to 768.

Explanation: 

we can evaluate the exponential expression and multiply the resulting value by 0.

10^2 means 10 multiplied by itself 2 times, which is:

10x10=100

Therefore, 0x 10^2 is equal to

0x100 0

So, 0x 10^2 simplifies to 0.

Explanation: 

we can evaluate each exponent and multiply the resulting values.

5^2 means 5 multiplied by itself 2 times, which is:

5x5=25

3^3 means 3 multiplied by itself 3 times, which is:

3x3x3=27

Therefore, 5^2 x 3^3 is equal to

25 x 27=675

So. 5^2 x 33 simplifies to 675.

Explanation: 

we can evaluate each exponent and multiply the resulting values

244 means 2 multiplied by itself 4 times, which ist

2×2×2×2=16

3^2 means 3 multiplied by itself 2 times, which is:

3×3-9

Therefore, 2^4 x 3^2 is equal to

16x9= 144

So, 2^4 x 3^2 simplifies to 144

Explanation:

we can evaluate each exponent and multiply the resulting values.

32 means 3 multiplied by itself 2 times, which is

3x3=9

10^4 means 10 multiplied by itself 4 times, which is:

10 x 10 x 10 x 10 = 10000

Therefore, 3^2 x 10^4 is equal to:

9 × 10000 90000

So, 32 x 104 simplifies to 90000.

Explanation: 

we need to evaluate the expression. The exponent 3 means we need to multiply -4 by itself three times:

(-4)=(-4) x (-4) x (-4)=-64

Therefore, (-4)? is equal to -64.

In words, (-4) means taking the number 4 and multiplying it by itself three times, which results in the value of -64.

Explanation:

we need to evaluate the expression inside the parentheses first. The exponent 3 means we need to multiply-2 by itself three times:

(-2)=(-2) x (-2) x (-2)=-8

Now we can substitute the value of (-2) into the expression:

=2^(-2)x3(4-5) x 4/1

=2^(-2) × 3^(-1)x4

=4/(2^2x 3)

Therefore, the simplified expression in exponential form is 4/2^2 x3)=2^(-2) × 3^(-1)=(1/2^2)

x (1/3^1)= 1/12, which is not equal to 3^2.

Explanation: 

To simplify ((542)3 x 54) 3^7 and express it in exponential form, we can use the product and

quotient rules of exponents:

((5^2)3 x 5^4)+5^75^(23) x 5^4+5^7

=5^6 × 5^4+5^7

= 5^(6+4-7)

5^3

Therefore, the simplified expression in exponential form is 5^3.

Explanation: 

To simplify 25^4+ 543 and express it in exponential form, we can write 25 as 542 and use the quotient rule of exponents:

25^4+5^3=(5^2)^5^3

=5^(24)+5^3

-548-543

5(8-3)

565

Therefore, the simplified expression in exponential form is 5^5.

Explanation:

we can simplify the expression as follows:

(3 × 72 × 11^8)/(21 x 11/3) = (7^2 x 11^8)/ (7 × 3 × 11^3)

=7^(2-1) x 11^(8-3)/3

=7x11^5/3

Multiplying by 7/7 to rationalize the denominator, we get:

=(7x11^5×7)/(3×7)

= 7 x 11^5

Therefore, the simplified expression in exponential form is 7x11^5.

Explanation:

To simplify (37)/ (3^4 x 343) and express it in exponential form, we can use the quotient rule of exponents, which states that when dividing two exponential expressions with the same base, we can subtract the exponents:

(347)/ (3^4 × 3^3)=37-4-3)

Any number raised to the power of 0 is equal to 1. so we have:

(347) (3^4 × 3^3) = 1

Therefore, the simplified expression in exponential form is 1.

Explanation: 

To simplify 2^0+30 + 40 and express it in exponential form, we can use the rule that any

number raised to the power of O is equal to 1:

2^0+30 +40=1+1+1

Therefore, the simplified expression in exponential form is 3.

Explanation:

To simplify 240 x 30 x 40 and express it in exponential form, we can use the rule that any number raised to the power of O is equal to 1:

240 x 30 x 40=1x1x1

Therefore, the simplified expression in exponential form is 1.

Explanation:

To simplify (30+20) x 50 and express it in exponential form, we can use the rule that any number raised to the power of 0 is equal to 1:

(30+20) x 50 = (1+1)*1

=2

Therefore, the simplified expression in exponential form is 2.

Explanation:

To simplify (2^8x^5)/(4^3 x a^3) and express it in exponential form, we can use the quotient rule of exponents and simplify the powers of 2 and 4:

(2^8 xa^5)/(4^3 x a^3)=(2^8x^5)/ (2^2)^3x^3

=(2^8x^5)/(2^6 x a^3)

= (2^(8-6)x^(5-3))

=2^2 xa^2

= 4^2

Therefore, the simplified expression in exponential form is 2^2,

Explanation:

To simplify (a 5/3)x a8 and express it in exponential form, we can simplify the expression inside the parentheses first

Then, we can use the product rule of exponents to simplify the entire expression:

(a^5/a^3) xa^=^2 xa^8

=a^(2+8)

Therefore, the simplified expression in exponential form is a^10.

Explanation:

we can first cancel out the common factors in the numerator and denominator:

(4^5 x a^8b^3) (4^5 x a^5b^2) = (a^8b+5)/(a^5^2)

Next, we can simplify the expression by dividing the powers of a and b

(a^8b^3)/(a^5b^2)=a^(8-5)x b^(3-2)=a^3 xb

Therefore, the simplified expression is a^3 x b.

Explanation:

we need to simplify the expression within the parentheses:

2^3=8

So we can rewrite the expression as:

(8 x 212

Then we simplify the expression within the parentheses again:

8x2=16

So the final expression is:

16^2

We can evaluate this by multiplying 16 by itself.

16^2=256

Therefore, (2^3 x 2)2=256.

Explanation:

We can simplify 10 x 10^11 by using the exponent rule that states a^ma'n=a^(m+n):

10x 10^11=10 (1+11) = 10^12

On the other hand, 10011 can also be simplified by using the exponent rule that states (am)^n= a^{m*n):

100^11 (10^2)^11 = 10^(211) = 10^22

Therefore, 10 x 10^11 is not equal to 100^11 because:

10 × 10^11 = 10^12

100^11 = 10^22

Hence. The statement 10 x 10^11 100 11" is false.

Explanation:

The statement "2^3> 5^2" is false.

We can simplify 2^3 to get

2^3=2×2×2=8

We can also simplify 5^2 to get:

5^2=5x5=25

Therefore, we can compare the two expressions:

2438

Since 8 is less than 25, we can conclude that 2^3 is not greater than 5^2. Hence, the statement 2^3>5^2" is false.

Explanation:

We can simplify the left-hand side of the equation us

2^3 × 3^2=8x9=72

However, when we simplify the right-hand side of the equation as:

65=6x6x6x6x6=7776

Since 72 is not equal to 7776, we can conclude that the statement 2^3 x 3^2=65 is false.

Explanation:

Any number raised to the power of O is equal to 1, regardless of the base. Therefore, we have:

3401

(1000) 01

Since both sides is equal to 1, we can conclude that the statement 30(1000)^0" is true.

Explanation:

Find the prime factorization of each number.

108=2^2 × 3^3

192=2^6 × 3^1

Multiply the prime factorizations together.

108 x 192 = (2^2 × 3^3) × (2^6 x 3^1)

Simplify the product by adding the exponents of the common factors.

108 x 192=2^(2+6) × 3^(3+1)

108 × 192 = 2^8 × 3^4

Therefore, 108 x 192 can be expressed as the product of prime factors 2^8 x 3^4 in exponential form

Explanation:

Find the prime factorization of the number.

270=2× 3^3 × 5

Write the prime factorization in exponential form

270=2^1 x 3^3 x 5^1

form.

Therefore, 270 can be expressed as the product of prime factors 2^1 × 3^3 x 5^1 in exponential

Explanation:

Find the prime factorization of each number.

729-36

6426

Multiply the prime factorizations together.

729 x 64 = 3^6 x 2^6

Simplify the product by adding the exponents of the common factors.

729 × 64 = (3 × 2)^6

729 x 6466

Therefore, 729 x 64 can be expressed as the product of prime factors 66 in exponential form.

Explanation:

Find the prime factorization of the number.

768=2^8 x 3

Write the prime factorization in exponential form.

768=2^83^1

Therefore, 768 can be expressed as the product of prime factors 248 x 341 in exponential form

Explanation:

First of all simplify the numerator.

((2^5)2 × 7^3)=(2^10 × 7^3)=2^10 × 343

Simplify the denominator.

(8^3 x7)=(2^3 x7)^3x7=56^3

Divide the numerator by the denominator.

((2^5)2 x 7^3)/ (8^3 x 7) = (2^10 x 343)/56^3

((2^5)2 x 7^3)/ (8^3 x 7)=98/1

Therefore, ((25)2 x 7^3)/(8^3 x 7) simplifies to 98.

Explanation:

Simplify the numerator.

245 x 5^2 x 1832 x 25 x 1^880018

Simplify the denominator.

10 3 x 14(2x 533 x 148 x 125 x 14 = 1000^4

Divide the numerator by the denominator.

(2^5 × 5^2 x1^8) (10^3 × 1^4) = (800^8)/(1000(4)

Simplify the fraction by canceling common factors.

(80018)/(100014) = (81^4 x 100^4)/(10^4 x 1001^4)

(800)/(1000)=(5)/(8)

Therefore, (251)/ (10) simplifies to (5)/8.

Explanation:

First, let's simplify the terms in the numerator and denominator separately

3^5 x 10^5 x 25 = 3^5 x (2 x 5)^5 x 25 = 3^5 x 25 x 5A7

5^7 × 6^5=5^7 × (2 × 3)^5=5^7 × 2^5 × 3^5

Now we can substitute these into the original expression:

(345 x 10^5 x 25)/(547 x 645)=(3^5 x 25 x 547)/(5^7 × 2^5 × 3^5)

We can then cancel out any common factors in the numerator and denominator

(345x2^5 x 5^7)/(5^7 x 2^5 × 3^5)=(3^5/3^5) x (2^5/2^5) × (5^7/5^7)

Simplifying further:

(345/3^5)=1

(2^5/2^5)=1

(5^7/5/7)=1

So we're left with

(345 x 10^5 x 25)/(57x65)=1x1x1=1 Therefore, the simplified expression is

Explanation:

To write the number 279404 in expanded form, we would separate each digit into its respective place value:

279404

11111+Ones (4)

1111+ Tens (0 x 10)

III Hundreds (4 x 100)

-Thousands (9x1000)

-Ten thousands (7 x 10,000)

Hundred thousands (2 x 100,000)

So, the expanded form of 279404 is:

2 x 100,000+7x 10,000+9x 1000+4 x 100 +0 x 10 +4 x 1

=200,000 +70,000+9000+400+0+4

=(2 x 10)+(7 x 10") + (9 x 10)+(4 x 10)+(0x10)+(4x 10°)

Explanation:

To write the number 3006194 in expanded form, we would separate each digit into its respective place value:

3006194

111111+-Ones (4)

HII+ Tens (9 x 10)

-Hundreds (1 x 100) -Thousands (6 x 1000)

-Ten thousands (0 x 10,000)

-Hundred thousands (3 x 100XXX)

So, the expanded form of 3006194 is:

= 3 x 100,000 +0 x 10,000 +0 x 1000+6 x 1000+1 x 100+9x10+4x1

=(3x10) + (0x10) + (0 x 10')+(6 x 10') + (1 x 10²) + (9 x 10') + (4 x 10)

Explanation:

To write the number 2806196 in expanded form, we would separate each digit into its respective place value:

2806196

IIIIII4 Ones (6)

1111+ Tens (9 x 10)

Hundreds (1 x 100)

-Thousands (6 x 1000)

-Ten thousands (0 x 10,000)

Hundred thousands (2 x 100,000)

So, the expanded form of 2806196 is:

=2x 100,000+ 8 x 10,000+0x 1000+6 x 1000 + 1 x 100+9 x 10+6x1

=(2 x 10)+(8 x 10)+(0x10)+(6x 10') + (1 x 10)+(9 x 10)+(6 x 10°)

Explanation:

To write the number 120719 in expanded form, we would separate each digit into its respective place value:

120719

11111+Ones (9)

III+ Tens (1 x 10)

111 Hundreds (7 x 100))

11+

-Thousands (0) x 1000)

-Ten thousands (2 x 10(XX)

Hundred thousands (0 x 100,000)

So, the expanded form of 120719 is:

=0x100,000+ 2 x 10,000+0x 1000+7x 100+ 1x 10+9x1

= (1 × 10)+(2 x 10)+(0x10)+(7 x 10)+(1 x 10)+(9 x 10%)

Explanation:

To write the number 20068 in expanded form, we would separate each digit into its respective place value:

20068

1111+-Ones (8)

(11+ Tens (6 x 10)

Hundreds (0 x 100)

-Thousands (0 x 1000)

Ten thousands (2 x 10,000)

So, the expanded form of 20068 is:

=2x 100X00+0x 1000+0x 100+6x10+8x1

=(2x 10)+(0x 10)+(0x10)+(6 x 10)+(8 × 10)

Explanation:

To find the number from the given expanded form, we simply multiply the coefficient of each term by its corresponding power of 10 and then add the results.

So, for (8 x 10)4+ (6 x 10)3 + (0 x 10)2 + (4 x 10)1 + (5 x 100, we have:

=8x10,000+6×1000+0x100+4x10+5x1

= 80,000+ 6,000+0+40+5

=86,045

Therefore, the number from the given expanded form is 86,045.

Explanation:

To find the number from the given expanded form, we simply multiply the coefficient of each term by its corresponding power of 10 and then add the results.

So, for (4 x 10)5+(5 x 10)3+ (3 x 1012+ (2 x 100), we have:

= 4 x 100000+5x1000+3 × 100+2×1

=400,000+ 5,000+300+2

=405,302

Explanation:

To find the number from the given expanded form, we simply multiply the coefficient of each term by its corresponding power of 10 and then add the results.

So, for (3 x 10)4+(7 x 10)2 + (5 x 100, we have:

= 3 x 10,000 +7 x 100+5x1

=30,000+700+5

=30,705

Therefore, the number from the given expanded form is 30,705.

Explanation:

To find the number from the given expanded form, we simply multiply the coefficient of each term by its corresponding power of 10 and then add the results.

So, for 19 x 10)5+ (2 × 10)2 + (3 × 10)1, we have:

=9x100,000+2×100+3×10

= 9,00,000+200+30

=9,00,230

Therefore, the number from the given expanded form is 9,000,230.

Explanation:

To express 5,00,00,000 in standard form, we need to determine the power of 10 by counting the number of zeros. There are 8 zeros, so the power of 10 is 8. the power of 8.

To convert the number to standard form, we need to multiply the coefficient (5) by 10 raised to Therefore, 500,00,000 in standard form is 5 x 10^8.

Explanation:

To express 70,00,000 in standard form, we need to determine the power of 10 by counting the number of zeros. There are 6 zeros, so the power of 10 is 6. the power of 6.

To convert the number to standard form, we need to multiply the coefficient (7) by 10 raised to

Explanation:

Therefore, 7000,000 in standard form is 7 x 10^6,

To express 3,18,65,00000 in standard form, we need to determine the power of 10 by counting the number of zeros. There are 10 zeros, so the power of 10 is 10.

To convert the number to standard form, we need to multiply the coefficient (3.1865) by 10 raised to the power of 10.

Therefore, 3,18,65,00,000 in standard form is 3.1865 x 10^10.

Explanation:

To express 390,878 in standard form, we need to determine the power of 10 by counting the number of zeros. There are Il zeros, so the power of 10 is 1.

To convert the number to standard forms, we need to multiply the coefficient (3.90878) by 10 mised to the power of 5.

Therefore, 390.878 in standard form is 3.90878 x 10^5.

Explanation:

To express 390878 in standard form, we need to determine the power of 10 by counting the number of digits to the left of the decimal point. There are 4 digits, so the power of 10 is 4.

To convert the number to standard form, we need to multiply the coefficient (3.90878) by 10 mised to the power of 4.

Therefore, 39087.8 in standard form is 3.90878 x 10^4

Explanation:

To express 3908.78 in standard form, we need to determine the power of 10 by counting the number of digits to the left of the decimal point. There are 3 digits, so the power of 10 is 3.

To convert the number to standard form, we need to multiply the coefficient (390878) by 10 raised to the power of 3.

Therefore, 39087.8 in standard form is 3.90878 x 10^3,

Explanation:

The distance between Earth and Moon is 384,000,000 m. The standard form of the number appearing in the given statement is 3.84 x 10^8 m. This is because standard form is a way to write large or small numbers in a more concise manner using powers of 10. In this case, we move the decimal point 8 places to the left and express the result as 3.84 x 10^8

Explanation:

The speed of light in a vacuum is 300.000.000 m/s. The standard form of the number appearing in the given statement is 3 x 10^8 m/s. This is because we move the decimal point 8 places to the left and express the result as 3 x 10^8, which is a more concise way of representing this large number.

Explanation:

The diameter of the Earth is 1,27,56000 m. The standard form of the number appearing in the given statement is 1.2756 x 10^7 m. This is because we move the decimal point 7 places to the left and express the results 1.2756 x 10^7, which is a more concise way of representing this large number.

Explanation:

The diameter of the Sun is 1,400,000 000 m. The standard form of the number appearing in the given statement is 14 x 10^9 m. This is because we move the decimal point 9 places to the left and express the result as 14 x 10^9, which is u more concise way of representing this large number.

Explanation:

In a galaxy, there are, on average, 100,000,000,000 stars. The standard form of the number appearing in the given statement is 1 x 10^11 stars. This is because we do not need to move the decimal point as the number is already in a concise form.

Explanation:

The statement. "The universe is estimated to be about 12000,000,000 years old" can be expressed in standard form as 1.2 x 10^10 years old. Standard form is a way to express a large or small number in a t a more concise and manageable way. In this case, the number is expressed in scientific notation where the base number is between 1 and 10 and the exponent is a power of 10.

Explanation:

The statement "The distance of the Sun from the center of the Milky Way Galaxy is estimated to he 300 000 000 000,000,000,000 m" can be expressed in standard form as 3x 10^20) m. This is because standard form is a way to express a very large or very small number in a more manageable way using scientific notation. In this case, the base number is 3 and the exponent is 20, indicating that the number is 3 multiplied by 10 twenty times.

Explanation:

The given statement mentions that a drop of water weighing 18 gm contains 60.230,000,000,000,000,000,000 molecules. This number can be expressed in standard form by first moving the decimal point to the left until only one non-zero digit remains to the left of the decimal point. This gives us 6023 as the coefficient. The power of 10 is obtained by counting the number of places the decimal point was moved to the left. In this case, the decimal point was moved 22 places to the left, so the power of 10 is 22. Therefore, the standard form of the number is 6/023 x 10^22 molecules.

Explanation:

The given statement mentions that the Earth has 1.353,000,000 cubic km of seawater. To express this number in standard form, we need to move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. This gives us 1353 as the coefficient. The decimal point needs to be moved 9 places to the left to get to this point, so the power of 10 is 9. Therefore. the standard form of the number is 1.353 x 10^9 cubic km.

Explanation:

The given statement mentions that the population of India was about 1027000,000 in March 2001.

To express this number in standard form, we need to move the decimal point to the left until there is only one non-zero digit to the left of the decimal point. This gives us 1.027 as the coefficient. The decimal point needs to be moved 9 places to the left to get to this point, so the power of 10 is 9. Therefore, the standard form of the number is 1.0127 x 10^9,