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Class 8

Explore popular questions from Exponents and Powers for Class 8. This collection covers Exponents and Powers previous year Class 8 questions hand picked by experienced teachers.

Exponents and Powers

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Q 1. The value of {tex} \left( \frac { - 1 } { 2 } \right) ^ { 4 } {/tex} is:

A

{tex} \frac { 1 } { 8 } {/tex}

B

{tex} \frac { - 1 } { 8 } {/tex}

{tex} \frac { 1 } { 16 } {/tex}

D

{tex} \frac { - 1 } { 16 } {/tex}

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Q 2. {tex} \left( \frac { 1 } { 3 } \right) ^ { 0 } {/tex} is equal to

A

{tex} \frac { 1 } { 3 } {/tex}

1

C

3

D

0

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Q 3. {tex} \left( \frac { 1 } { 2 } \right) ^ { 3 } \times \left( \frac { 1 } { 3 } \right) ^ { 3 } {/tex} is equal to

{tex} \frac { 1 } { 216 } {/tex}

B

{tex} \frac { 1 } { 125 } {/tex}

C

{tex} \frac { 1 } { 54 } {/tex}

D

None of these

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Q 4. When simplified {tex} 7 ^ { 0 } \times 5 ^ { 0 } , {/tex} we get

1

B

0

C

35

D

None of these

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Q 5. Which of the following is true?

A

{tex} \left[ \left( \frac { \mathrm { a } } { \mathrm { b } } \right) ^ { \mathrm { m } } \right] ^ { \mathrm { n } } = \left( \frac { \mathrm { a } } { \mathrm { b } } \right) ^ { \mathrm { m } + \mathrm { n } } {/tex}

{tex} \left[ \left( \frac { \mathrm { a } } { \mathrm { b } } \right) ^ { \mathrm { m } } \right] ^ { \mathrm { n } } = \left( \frac { \mathrm { a } } { \mathrm { b } } \right) ^ { \mathrm { mn } } {/tex}

C

{tex} \left( \frac { \mathrm { a } } { \mathrm { b } } \right) ^ { 0 } = 0 {/tex}

D

{tex} \left( \frac { \mathrm { a } } { \mathrm { b } } \right) ^ { \mathrm { n } } = \frac { 1 } { \left( \frac { \mathrm { a } } { \mathrm { b } } \right) ^ { \mathrm { n } } } {/tex}

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Q 6. If n is an odd positive integer, then {tex} ( - 1 ) ^ { n } {/tex} is equal to

A

1

B

0

{tex} - 1 {/tex}

D

None of these

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Q 7. Which of the following is not equal to {tex} \frac { - 8 } { 27 } ? {/tex}

{tex} \left( \frac { 2 } { 3 } \right) ^ { - 3 } {/tex}

B

{tex} - \left( \frac { 2 } { 3 } \right) ^ { 3 } {/tex}

C

{tex} \left( \frac { - 2 } { 3 } \right) ^ { 3 } {/tex}

D

{tex} \left( \frac { - 2 } { 3 } \right) \times \left( \frac { - 2 } { 3 } \right) \times \left( \frac { - 2 } { 3 } \right) {/tex}

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Q 8. {tex} \left( \frac { 2 } { 3 } \right) ^ { - 5 } {/tex} is equal to

A

{tex} \left( \frac { - 2 } { 3 } \right) ^ { 5 } {/tex}

{tex} \left( \frac { 3 } { 2 } \right) ^ { 5 } {/tex}

C

{tex} \frac { 2 \times ( - 5 ) } { 3 } {/tex}

D

{tex} \frac { 2 } { 3 \times 5 } {/tex}

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Q 9. {tex} \left( \frac { - 3 } { 2 } \right) ^ { - 1 } {/tex} is equal to

A

{tex} \frac { 2 } { 3 } {/tex}

{tex} - \frac { 2 } { 3 } {/tex}

C

{tex} \frac { 3 } { 2 } {/tex}

D

None of these

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Q 10. {tex} \left( - \frac { 1 } { 5 } \right) ^ { 3 } \div \left( - \frac { 1 } { 5 } \right) ^ { 8 } {/tex} is equal to

A

{tex} \left( - \frac { 1 } { 5 } \right) ^ { 5 } {/tex}

B

{tex} \left( - \frac { 1 } { 5 } \right) ^ { 11 } {/tex}

{tex} ( - 5 ) ^ { 5 } {/tex}

D

{tex} \left( \frac { 1 } { 5 } \right) ^ { 5 } {/tex}

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Q 11. For a non-zero rational number a, {tex} \mathrm { a } ^ { 7 } \div \mathrm { a } ^ { 12 } {/tex} is equal to

A

{tex} a ^ { 5 } {/tex}

B

{tex} a ^ { - 19 } {/tex}

{tex} a ^ { - 5 } {/tex}

D

{tex} a ^ { 19 } {/tex}

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Q 12. The value of {tex} \left( \frac { 4 } { 3 } \right) ^ { - 6 } \div \left( \frac { 4 } { 3 } \right) ^ { - 6 } {/tex} is

A

{tex} \frac { - 4 } { 3 } {/tex}

1

C

0

D

{tex} \left( \frac { - 4 } { 3 } \right) ^ { - 12 } {/tex}

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Q 13. For a non-zero rational number a, {tex} \left( a ^ { 3 } \right) ^ { - 2 } {/tex} is equal to

A

{tex} a ^ { 6 } {/tex}

{tex} a ^ { - 6 } {/tex}

C

{tex} a ^ { - 9 } {/tex}

D

{tex} a ^ { 5 } {/tex}

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Q 14. The value of {tex} \left( 7 ^ { - 1 } - 8 ^ { - 1 } \right) ^ { - 1 } - \left( 3 ^ { - 1 } - 4 ^ { - 1 } \right) ^ { - 1 } {/tex} is

A

56

B

12

C

68

44

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Q 15. The value of {tex} x {/tex} to make the statement {tex} \left( \frac { 5 } { 9 } \right) ^ { - 2 } \times \left( \frac { 18 } { 25 } \right) ^ { - 2 } = x ^ { - 2 } {/tex} true, is

A

{tex} \frac { 5 } { 2 } {/tex}

B

{tex} \left( \frac { 5 } { 2 } \right) ^ { - 2 } {/tex}

C

{tex} \left( \frac { - 5 } { 2 } \right) ^ { 4 } {/tex}

{tex} \frac { 2 } { 5 } {/tex}

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Q 16. If {tex} \frac { x } { y } = \left( \frac { 2 } { 5 } \right) ^ { - 3 } \times \left( \frac { 15 } { 8 } \right) ^ { - 3 } , {/tex} then {tex} \left( \frac { x } { y } \right) ^ { - 1 } {/tex} is equal to

{tex} \frac { 27 } { 64 } {/tex}

B

{tex} \frac { 81 } { 64 } {/tex}

C

{tex} \frac { - 81 } { 64 } {/tex}

D

{tex} \frac { - 16 } { 81 } {/tex}

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Q 17. If {tex} x = \left( 8 ^ { \frac { 2 } { 3 } } \cdot 32 ^ { - \frac { 2 } { 5 } } \right) , {/tex} then {tex} x ^ { - 5 } = {/tex}

A

{tex} \frac { 1 } { 32 } {/tex}

B

{tex} - 1 {/tex}

1

D

{tex} - 5 {/tex}

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Q 18. {tex} 81 ^ { \frac { 1 } { 4 } } \times 9 ^ { \frac { 3 } { 2 } } \times 27 ^ { - \frac { 4 } { 3 } } = {/tex}

1

B

3

C

9

D

{tex} \frac { 1 } { 3 } {/tex}

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Q 19. If {tex} 4 ( 4 x ) ^ { 7 } = 4 ^ { 6 ^ { 2 } } , {/tex} then what is the value of {tex} x ? {/tex}

A

5

B

25

C

64

256

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Q 20. {tex} \sqrt [ 5 ] { 0.03125 } = {/tex}

A

0.25

0.5

C

0.126

D

0.15

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Q 21. Find the value of {tex} ( 0.000064 ) ^ { \frac { 2 } { 3 } } \div ( 0.0016 ) ^ { \frac { 3 } { 4 } } {/tex}

A

{tex} 3 ^ { - 1 } {/tex}

B

{tex} 4 ^ { - 1 } {/tex}

{tex} 5 ^ { - 1 } {/tex}

D

{tex} 10 ^ { - 1 } {/tex}

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Q 22. Find the value of {tex} ( 6561 ) ^ { ( 0.125 ) } + ( 3125 ) ^ { 0.2 } {/tex}

A

4

B

6

8

D

None of these

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Q 23. If {tex} \frac { - 4 } { x } = \frac { x } { 16 } , {/tex} then {tex} x {/tex} is

A

A rational number

B

An integer

C

A natural number

Not a rational number

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Q 24. Form the number from this expanded form:
{tex} 3 \times \frac { 1 } { 10 } + 4 \times \frac { 1 } { 10 ^ { 2 } } + 6 \times \frac { 1 } { 10 ^ { 4 } } + 3 \times \frac { 1 } { 10 ^ { 5 } } {/tex}

A

3463

0.34063

C

34.63

D

34063