The correct option is C 2^8 ((2^2)^2)^2 nbsp;=(2^2)^2 × 2 nbsp; nbsp; nbsp; nbsp; nbsp;[∵ (a^n)^m = (a)^m × n] =(2^2)^4 =2^(2 × 4) =2^8 ...

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Power Law

The value of ...

Question

The value of ${({(2^{2})}^{2})}^{2}$ is:

$2^{6}$

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$2^{16}$

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$2^{8}$

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$2^{4}$

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Solution

The correct option is C
$2^{8}$

${({(2^{2})}^{2})}^{2}$

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

$= {(2^{2})}^{4}$

$= 2^{(2 \times 4)}$

$= 2^{8}$

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