Chapter 6 - Radical Functions and Rational Exponents - 6-4 Rational Exponents - Practice and Problem-Solving Exercises - Page 386: 49

$4$

We are asked to simplify: $(-8)^{\frac{2}{3}}$ Since $(-2)^3=-8$, then: $\left(-8\right)^{\frac{2}{3}}=\left[(-2)^3\right]^{\frac{2}{3}}$ Now, recall the basic exponent property (pg. 360): $(a^m)^n=a^{mn}$ Applying this property, we get: \begin{align*} \left[(-2)^3\right]^{\frac{2}{3}}&=(-2)^{\frac{3 \cdot 2}{3}}\\ &=(-2)^{\frac{6}{3}}\\ &=(-2)^2\\ &=4 \end{align*}