Simplify (y^(2/3))^-9

${(y^{\frac{2}{3}})}^{- 9}$

Step 1

Multiply the exponents in ${(y^{\frac{2}{3}})}^{- 9}$ .

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

$y^{\frac{2}{3} \cdot - 9}$

Cancel the common factor of $3$ .

Factor $3$ out of $- 9$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y^{2 \cdot - 3}$

Multiply $2$ by $- 3$ .

$y^{- 6}$

Step 2

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

$\frac{1}{y^{6}}$