Simplify (x^-3)^(2/5)

${(x^{- 3})}^{\frac{2}{5}}$

Step 1

Multiply the exponents in ${(x^{- 3})}^{\frac{2}{5}}$ .

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

$x^{- 3 (\frac{2}{5})}$

Multiply $- 3 (\frac{2}{5})$ .

Combine $- 3$ and $\frac{2}{5}$ .

$x^{\frac{- 3 \cdot 2}{5}}$

Multiply $- 3$ by $2$ .

$x^{\frac{- 6}{5}}$

Move the negative in front of the fraction.

$x^{- \frac{6}{5}}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{\frac{6}{5}}}$