Find the value of $m - n$ such that $a^{m} = a^{n}$ .

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Solution

Given,
$a^{m} = a^{n}$

$\frac{a^{m}}{a^{n}} = 1$

We know that, $\frac{a^{m}}{a^{n}} = a^{m - n}$

$a^{m - n} = 1$

$a^{m - n} = a^{0}$

As the bases are same, equating the powers

$m - n = 0$ .

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