Answer
$\dfrac{1}{16}$
Work Step by Step
Since $2^5=32$, then:
$32^{-\frac{4}{5}}=(2^5)^{-\frac{4}{5}}$
Now, recall the basic exponent property (pg. 360):
$(a^m)^n=a^{mn}$
Applying this property, we get:
$(2^5)^{-\frac{4}{5}}=2^{\frac{-5\cdot4}{5}}=2^{-4}$
Next, recall the basic property of negative exponents (pg. 383):
$a^{-m}=\frac{1}{a^m}$
Applying this property, we get:
\begin{align*}
2^{-4}&=\frac{1}{2^4}\\\\
&=\frac{1}{16}\\
\end{align*}
