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

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

Step 1

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

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

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

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

$x^{\frac{2}{3} \cdot (3 (- 1))}$

Cancel the common factor.

$x^{\frac{2}{3} \cdot (3 \cdot - 1)}$

Rewrite the expression.

$x^{2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$x^{- 2}$

Step 2

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

$\frac{1}{x^{2}}$