Answer
$\frac{1}{16}$
Work Step by Step
$$32^{-\frac{4}{5}}$$
Remember, a negative exponent can be made positive by moving the expression from the numerator to the denominator (or vise-versa).
$$=\frac{1}{32^{\frac{4}{5}}}$$
When converting from a rational exponent to a radical, the numerator is the exponent, and the denominator is the radicals index. It may be easier to have the entire radical raised to the exponent rather than the radicand.
As example: $\sqrt[5]{32^4}$ would be very difficult to solve, therefore:
$$=\frac{1}{(\sqrt[5]{32})^{4}}$$ $$=\frac{1}{(2)^{4}}$$ $$=\frac{1}{16}$$
