Is ${(a^{m})}^{n} = {(a^{n})}^{m}$ Explain.

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Solution

Show that $(a^{m})^{n} = (a^{n})^{m}$
Taking LHS.
$= (a^{m})^{n}$
$= a^{m n}$ (According to properties of exponets)
Taking $R H S$ .
$= (a^{n})^{m}$
$= a^{n m}$ (According to properties of exponents)
$= a^{m n}$
$= L H S$
$L H S = R H S$

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