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Exponents with like Bases

Question 31In...

Question

Question 31

In the following question, out of the four options, only one is correct. Write the correct answer.

For a non-zero rational number $z, (z^{- 2})^{3}$ is equal to:

(a) $z^{6}$

(b) $z^{- 6}$

(c) $z^{1}$

(d) $z^{4}$

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Solution

Using law of exponents , $(a^{m})^{n} = (a)^{m n}$
Similarly , $(z^{- 2})^{3} = (z)^{(- 2) \times 3} = (z)^{- 6}$

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Question 30

In the following question, out of the four options, only one is correct. Write the correct answer.

For a non-zero rational number $p^{13} \div p^{8}$ is equal to :

(a) $p^{5}$

(b) $p^{21}$

(d) $p^{- 19}$

Question 29

In the following question, out of the four options, only one is correct. Write the correct answer.

For any two non-zero rational numbers x and $y, x^{4} \div y^{4}$ is equal to:

(a) $(x \div y)^{0}$

(b) $(x \div y)^{1}$

(d) $(x \div y)^{8}$

Question 22

In the following question, out of the four options, only one is correct. Write the correct answer:

For a non-zero integer x, $(x^{4})^{- 3}$ is equal to:
(a) $x^{12}$
(b) $x^{- 12}$
(c) $x^{64}$
(d) $x^{- 64}$

Question 21

In the following question, out of the four options, only one is correct. Write the correct answer:

For a non-zero integer $x, x^{7} \div x^{12}$ is equal to:
(a) $x^{5}$
(b) $x^{19}$
(c) $x^{- 5}$
(d) $x^{- 19}$

Question 13

In the following question, out of the four options, only one is correct. Write the correct answer:

If y be any non-zero integer, then $y^{0}$ is equal to:
(a) 1
(b) 0
(c) -1
(d) Not defined

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