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

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Solution

Formula: 1 Mark
Value of n: 1 Mark
Numerical value: 1 Mark
Steps: 1 Mark

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.

$\Rightarrow 2 m n = 2 m$

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

$\Rightarrow n = 1$

As per question,
a=2 and m=4
On substituting the values, we get:
$a^{2 m}$ = $2^{2 \times 4}$
= $2^{8}$
= $2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$
= $256$
Hence, the required value is 256.

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