If $15625 = (x)^{2} = 5^{(y)}$ . Find the value of $x$ and $y$ .

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Solution

$15625 = (x)^{2} = 5^{(y)}$
Prime factorisation of
$15625 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 5^{6} = {(5^{3})}^{2}$
$= 125^{2}$
$\Rightarrow x = 125$
$\Rightarrow y = 6$

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