Find the value of $m$ for which $5^{m} / 5^{- 3} = 5^{5} .$

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Solution

$\frac{5^{m}}{5^{- 3}} = 5^{5}$
$\Rightarrow 5^{m} = 5^{5} \times 5^{- 3} = 5^{2}$
$\Rightarrow m = 2$

When the bases are same, the powers can be equated.

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