If ${(2^{m})}^{4} = 4^{6}$ , find the value of $m$ .

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Solution

${(2^{m})}^{4} = 4^{6}$
$2^{m 4} = {(2^{2})}^{6}$
$2^{m 4} = 2^{12}$
$4 m = 12$
$m = \frac{12}{4} = 3$

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If (2m)4=46, find the value of m.

(2m)4=46 2m4=(22)6 2m4=212 4m=12 m=124=3

If ${(2^{m})}^{4} = 4^{6}$ , find the value of $m$ .

${(2^{m})}^{4} = 4^{6}$
$2^{m 4} = {(2^{2})}^{6}$
$2^{m 4} = 2^{12}$
$4 m = 12$
$m = \frac{12}{4} = 3$