Chapter 6 - Radical Functions and Rational Exponents - 6-4 Rational Exponents - Practice and Problem-Solving Exercises - Page 386: 50

$64$

Since $(-2)^5=-32$, then: $(-32)^{\frac{6}{5}}=\left[(-2)^5\right]^{\frac{6}{5}}$ Now, recall the basic exponent property (pg. 360): $(a^m)^n=a^{mn}$ Applying this property, we get: \begin{align*} \left[(-2)^5\right]^{\frac{6}{5}}&=(-2)^{\frac{5\cdot6}{5}}\\ &=(-2)^{\frac{30}{5}}\\ &=(-2)^6 &=64 \end{align*}