Question

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

Answer 1

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

Since the bases on both the sides are equal, therefore the exponents must also be equal.

$\Rightarrow$ $m+1+5=-4$
$\Rightarrow$$m=-10$.
(1 mark)