Question

# Simplify $\frac{64}{125}$ raised to the power $\frac{-2}{3}$.

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Solution

## Simplify $\frac{64}{125}$ raised to the power $\frac{-2}{3}$. Simplify using properties of power and exponents:$\begin{array}{c}{\left(\frac{64}{125}\right)}^{\frac{-2}{3}}={\left(\frac{125}{64}\right)}^{\frac{2}{3}}\\ ={\left({\left(\frac{125}{64}\right)}^{\frac{1}{3}}\right)}^{2}\\ ={\left({\left(\frac{5}{4}\right)}^{3×\frac{1}{3}}\right)}^{2}\\ ={\left(\frac{5}{4}\right)}^{2}\\ =\frac{25}{16}\end{array}$Hence, the simplification$\frac{64}{125}$ raised to the power $\frac{-2}{3}$is$\frac{25}{16}$.

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