Question

If $(2{)}^{m+1}\times 2^5=4^{-2}$, then the value of $m$ is _____.

• A. -4
• B. -6
• C. -8
• D. -10

Answer 1

The correct option is D

-10

Given, $(2{)}^{m+1}\times 2^5=4^{-2}$
$\Rightarrow$ $(2{)}^{m+1}\times 2^5={\left(\right(2{)}^2)}^{-2}$
$\Rightarrow$ $(2{)}^{m+1+5}=(2{)}^{-4}$
Since the bases on both the sides are equal, therefore the exponents must also be equal. This means, $m+1+5=-4$, or $m=-10$.