Find the value of 'n' if ${(a^{m})}^{2 n} = a^{2 m}$ [4 MARKS]

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Solution

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

Given that,

${(a^{m})}^{2 n} = a^{2 m}$

$a^{2 m n} = a^{2 m}$ $[∵ {(a^{m})}^{n} = a^{m n}]$

Since bases are same, their exponents also should be equal.

$\Rightarrow 2 m n = 2 m$

$\Rightarrow n = \frac{2 m}{2 m}$

$\Rightarrow n = 1$

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