Answer
$x=-5$
Work Step by Step
The given expression, $
2^x=\dfrac{1}{32}
,$ is equivalent to
\begin{align*}
2^x&=\dfrac{1}{2^5}
\\\\
2^x&=2^{-5}
&\left(\dfrac{1}{x^{a}}=x^{-a}\right)
.\end{align*}
With both sides of the equation expressed in the same base, the exponents can be equated. That is,
\begin{align*}
x=-5
.\end{align*}
