Question

If $(2{)}^{m+1}\times 2^5=4^3$ the value of $m$ is

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Answer 1

Given, $(2{)}^{m+1}\times 2^5=4^3$
$\Rightarrow$ $(2{)}^{m+1}\times 2^5={\left(\right(2{)}^2)}^3$

$\because a^m\times a^n=a^{(m+n)}$
$\Rightarrow$ $(2{)}^{m+1+5}=(2^2{)}^3$

$\because (a^m{)}^n=(a{)}^{(m\times n)}$

$\Rightarrow$ $(2{)}^{m+1+5}=(2{)}^6$
Equating the powers.

$m+1+5=6$

$\Rightarrow m=0$.