Simplify the Radical Expression (z^(-4/3))^(-6/5)

${(z^{- \frac{4}{3}})}^{- \frac{6}{5}}$

Step 1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$z^{- \frac{4}{3} (- \frac{6}{5})}$

Step 2

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$z^{\frac{- 4}{3} (- \frac{6}{5})}$

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$z^{\frac{- 4}{3} \cdot \frac{- 6}{5}}$

Factor $3$ out of $- 6$ .

$z^{\frac{- 4}{3} \cdot \frac{3 (- 2)}{5}}$

Cancel the common factor.

$z^{\frac{- 4}{3} \cdot \frac{3 \cdot - 2}{5}}$

Rewrite the expression.

$z^{- 4 (\frac{- 2}{5})}$

Step 3

Combine $- 4$ and $\frac{- 2}{5}$ .

$z^{\frac{- 4 \cdot - 2}{5}}$

Step 4

Multiply $- 4$ by $- 2$ .

$z^{\frac{8}{5}}$