## Exponents and Powers Extra Questions with Answers

**Exponents and powers extra questions** play a vital role in strengthening the maths
concepts. After studying the concepts of mathematics, revision of questions related
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## Exponents and Powers** Worksheet 1 with Answers**

**1.
**State true or false for each of the following:

a.
13^{2} – 12^{2} = 5^{2}

b.
Cube root of 5^{9}/3^{12} is 5^{3}/3^{6}.

c. The least number by which 5400 must
be multiplied so as to make it a perfect cube is 5.

d. Cube of 0.6 is
0.0216.

**2.
**Evaluate: (–5)^{6 }× (–5)^{2}
× (–5)^{1} × (–5)^{0}

**3.
**Fill in the blanks.

a.
The result of 10^{3} + 9^{3} and 12^{3} + 1^{3}
are __________.

b.
The cube root of 3375 is _________.

c.
3^{2 }× 4^{2} is greater than 2^{3} × 2^{4} by
_________.

**4.
**Find the sum of squares of first five odd
numbers.

**5. **Find the cube root of

a. 2^{12}/3^{6}

b. 3^{0}/5^{9}

**6. **Find the value of 3 × (–2)^{2}.

**7.
**Choose the correct answer for each of the
following.

a.
2^{2} × 2^{3} × 2^{5} written in exponential form is

i.
2^{10}

ii. 2^{8}

iii. 2^{30}

iv. 2^{15}

b.
4 × 16 × 32 written in exponential form is

i.
4^{5}

ii. 2^{7}

iii. 2^{11}

iv. 8^{4 }

c.
2^{0} × (2)^{3} × 3^{3} is equal to

i. –216

ii. –72

iii. 216

iv. –432

d.
Square root of 225/784 is

i. 25/28

ii. 15/24

iii. 25/24

iv. 15/28

## Exponents and Powers** Worksheet 2 ****with Answers**

**1**. Fill in the blanks:

a.
3^{11 }× 3^{–8} = ___________

b.
The cube of –2 is ___________.

c.
The square root of 64 is ___________.

d.
2^{3} + 3 =___________

e.
The square of 8 is equal the cube of ___________.

**2.
**Express the following in exponential form:

a. 25600

b. 23716

**3.
**Simplify:

a.
(3^{5} × 2^{4}) ÷ (2^{2} × 3^{2})

b.
(2^{9} × 2^{11}) ÷ 2^{7 }

**4.
**Evaluate: 5^{3} + 2^{5} – 3^{4}

**5.
**Find the number whose square is equal to the
sum of the squares of 3 and 4.

**6.
**Find the sum of squares of first four odd
prime numbers.

**7. **Find the number whose cube is 1 less than the sum of the cubes of
9 and 10.

## Exponents and Powers** Worksheet 3 ****with Answers**

**1.
**Find the product of (–3)^{3} × 2^{4}
× (7)^{0} × 5^{2}.

**2.
**Find the least number that must be added to
222 for it to be a perfect square.

**3.
**Fill in the blanks of each of the following:

a.
2^{3} × 3^{2} × 5^{0} is equal to __________.

b.
(+4)^{3} is __________ (+2)^{5}

c. (−2) × (−2) × (−2) × (−4) × (−4) ×
(−8) × (−8) expressed in exponential form is equal to ____________.

d.
972 expressed in exponential form is equal to __________.

**4.
**Find the square root of:

i. 18225

ii. 441

**5.
**State whether the following statements are
true or false.

a.
(+15)^{0} is greater than (–8)^{0}.

b.
512 expressed in powers of 2 is equal to 2^{9}.

c.
(243)^{5} has 243 as base and 5 as its exponent.

d.
3969 expressed as product of the powers of their prime factors is 7^{2}
× 3^{3}.

**6.
**Choose the correct answer for each of the
following:

a.
Cube root of 9261 is

i. 21

ii. 441

iii. 63

iv. 147

b.
Cube of −4/7 is

i. 64/49

ii. 64/343

iii. −64/343

iv. 16/49

c.
2^{2} + 2^{3} + 2^{4} is equal to

i.
2^{9}

ii. 28

iii. 21

iv. 256

d.
The least number that must be multiplied by 1323 to make it a perfect square is

i. 3

ii. 9

iii. 7

iv. 21

**7.
**Find the cube of 3/5.

**8.
**Find the square root of 81/625.

**9.
**Write the prime factorization of each of the
following numbers in exponential form:

i. 5004

ii. 42336

**10. **Find the sum of squares of first five whole
numbers.

**ANSWERS**

**Worksheet 1**

1. a. True b. False

c. True
d. False

2. –1953125

3. a. 1729 b. 15

c. 16

4. 165

5. a. 16/9 b. 1/125

6. 12

7. a. i b. iii

c. iii
d. iv

**Worksheet 2 **

1. a. 3^{3 }b. –8

c. 8
d. 11

e. 4

2. a. 2^{10} × 5^{2}

b. 2^{2} × 7^{2} × 11^{2}

3. a. 108 b. 8192

4. 76

5. 5

6. 204

7. 12

**Worksheet 3**

1. –10800

2. 3 ** **

3. a. 72

b. greater than

c. (–2)^{13}

d. 2^{2} × 3^{5}

4. i. 135 ii. 21

5. a. False b.
True

c. True d. False

6. a. i b. iii

c. ii d. i

7. 27/125

8. 9/25

9. i. 2^{2 }× 3^{2 }×
139

ii. 2^{5} × 3^{3} × 7^{2}

10. 30

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