Simplify ((x^6)/(y^9))^(-1/3)

${(\frac{x^{6}}{y^{9}})}^{- \frac{1}{3}}$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{y^{9}}{x^{6}})}^{\frac{1}{3}}$

Step 2

Apply the product rule to $\frac{y^{9}}{x^{6}}$ .

$\frac{{(y^{9})}^{\frac{1}{3}}}{{(x^{6})}^{\frac{1}{3}}}$

Step 3

Multiply the exponents in ${(y^{9})}^{\frac{1}{3}}$ .

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

$\frac{y^{9 (\frac{1}{3})}}{{(x^{6})}^{\frac{1}{3}}}$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$\frac{y^{3 (3) \frac{1}{3}}}{{(x^{6})}^{\frac{1}{3}}}$

Cancel the common factor.

$\frac{y^{3 \cdot 3 \frac{1}{3}}}{{(x^{6})}^{\frac{1}{3}}}$

Rewrite the expression.

$\frac{y^{3}}{{(x^{6})}^{\frac{1}{3}}}$

Step 4

Multiply the exponents in ${(x^{6})}^{\frac{1}{3}}$ .

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

$\frac{y^{3}}{x^{6 (\frac{1}{3})}}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factor.

$\frac{y^{3}}{x^{3 \cdot 2 \frac{1}{3}}}$

Rewrite the expression.

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