Find the value of $m$ for which $5^{m} \div 5^{- 3} = 5^{5}$

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Solution

$5^{m} \div 5^{- 3} = 5^{5}$
$\Rightarrow 5^{m} \div \frac{1}{5^{3}} = 5^{5}$
$\Rightarrow 5^{m} \times 5^{3} = 5^{5}$
$\Rightarrow 5^{m + 3} = 5^{5}$
$\Rightarrow m + 3 = 5$
$\Rightarrow m = 5 - 3 = 2$

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