Simplify 5(x^(2/3))^-1

$5 {(x^{\frac{2}{3}})}^{- 1}$

Step 1

Multiply the exponents in ${(x^{\frac{2}{3}})}^{- 1}$ .

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

$5 x^{\frac{2}{3} \cdot - 1}$

Multiply $\frac{2}{3} \cdot - 1$ .

Combine $\frac{2}{3}$ and $- 1$ .

$5 x^{\frac{2 \cdot - 1}{3}}$

Multiply $2$ by $- 1$ .

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

Move the negative in front of the fraction.

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

Step 2

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

$5 \frac{1}{x^{\frac{2}{3}}}$

Step 3

Combine $5$ and $\frac{1}{x^{\frac{2}{3}}}$ .

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