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Exponent of an Exponent

5-2 can also ...

Question

$5^{- 2}$ can also be expressed as

\frac{1}{25}

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\frac{1}{5^{- 2}}

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\frac{1}{5}

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None of these

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Solution

The correct option is A $\frac{1}{25}$
$5^{- 2} = 5^{- 1 * 2}$

$= (5^{2})^{- 1}$ $∵ (a)^{m n} = (a^{m})^{n}$

$= \frac{1}{5^{2}}$ $∵ a^{- n} = \frac{1}{a^{n}}$

$= \frac{1}{25}$

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