Which one of the following options is the multiplicative inverse of $2^{5}$ ?

(- 2)^{- 5}

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2^{- 5}

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5^{- 2}

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5^{2}

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Solution

The correct option is B $2^{- 5}$
Since $x \times \frac{1}{x} = 1,$ the multiplicative inverse of any non-zero $x$ isgiven by $\frac{1}{x} .$

Hence, the multiplicative inverse of $2^{5}$ is $\frac{1}{2^{5}} .$
But, $\frac{1}{2^{5}} = 2^{- 5}$ as $\frac{1}{a^{m}} = a^{- m} .$
Thus, the multiplicative inverse of $2^{5}$ is $2^{- 5} .$

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Which one of the following options is the multiplicative inverse of 25?

The correct option is B 2−5Since x×1x=1, the multiplicative inverse of any non-zero x isgiven by 1x. Hence, the multiplicative inverse of 25 is 125. But, 125=2−5 as 1am=a−m. Thus, the multiplicative inverse of 25 is 2−5.

Which one of the following options is the multiplicative inverse of $2^{5}$ ?