Simplify ((9x^(-2/3)y^(-1/3))/(xy^-3))^-3

${(\frac{9 x^{- \frac{2}{3}} y^{- \frac{1}{3}}}{x y^{- 3}})}^{- 3}$

Move $x^{- \frac{2}{3}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{9 y^{- \frac{1}{3}}}{x y^{- 3} x^{\frac{2}{3}}})}^{- 3}$

Multiply $x$ by $x^{\frac{2}{3}}$ by adding the exponents.

Move $x^{\frac{2}{3}}$ .

${(\frac{9 y^{- \frac{1}{3}}}{x^{\frac{2}{3}} x y^{- 3}})}^{- 3}$

Multiply $x^{\frac{2}{3}}$ by $x$ .

Raise $x$ to the power of $1$ .

${(\frac{9 y^{- \frac{1}{3}}}{x^{\frac{2}{3}} x^{1} y^{- 3}})}^{- 3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{9 y^{- \frac{1}{3}}}{x^{\frac{2}{3} + 1} y^{- 3}})}^{- 3}$

Write $1$ as a fraction with a common denominator.

${(\frac{9 y^{- \frac{1}{3}}}{x^{\frac{2}{3} + \frac{3}{3}} y^{- 3}})}^{- 3}$

Combine the numerators over the common denominator.

${(\frac{9 y^{- \frac{1}{3}}}{x^{\frac{2 + 3}{3}} y^{- 3}})}^{- 3}$

Add $2$ and $3$ .

${(\frac{9 y^{- \frac{1}{3}}}{x^{\frac{5}{3}} y^{- 3}})}^{- 3}$

Move $y^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{9 y^{- \frac{1}{3}} y^{3}}{x^{\frac{5}{3}}})}^{- 3}$

Multiply $y^{- \frac{1}{3}}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

${(\frac{9 (y^{3} y^{- \frac{1}{3}})}{x^{\frac{5}{3}}})}^{- 3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{9 y^{3 - \frac{1}{3}}}{x^{\frac{5}{3}}})}^{- 3}$

To write $3$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

${(\frac{9 y^{3 \cdot \frac{3}{3} - \frac{1}{3}}}{x^{\frac{5}{3}}})}^{- 3}$

Combine $3$ and $\frac{3}{3}$ .

${(\frac{9 y^{\frac{3 \cdot 3}{3} - \frac{1}{3}}}{x^{\frac{5}{3}}})}^{- 3}$

Combine the numerators over the common denominator.

${(\frac{9 y^{\frac{3 \cdot 3 - 1}{3}}}{x^{\frac{5}{3}}})}^{- 3}$

Simplify the numerator.

Multiply $3$ by $3$ .

${(\frac{9 y^{\frac{9 - 1}{3}}}{x^{\frac{5}{3}}})}^{- 3}$

Subtract $1$ from $9$ .

${(\frac{9 y^{\frac{8}{3}}}{x^{\frac{5}{3}}})}^{- 3}$

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

${(\frac{x^{\frac{5}{3}}}{9 y^{\frac{8}{3}}})}^{3}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{x^{\frac{5}{3}}}{9 y^{\frac{8}{3}}}$ .

$\frac{{(x^{\frac{5}{3}})}^{3}}{{(9 y^{\frac{8}{3}})}^{3}}$

Apply the product rule to $9 y^{\frac{8}{3}}$ .

$\frac{{(x^{\frac{5}{3}})}^{3}}{9^{3} {(y^{\frac{8}{3}})}^{3}}$

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

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

$\frac{x^{\frac{5}{3} \cdot 3}}{9^{3} {(y^{\frac{8}{3}})}^{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{x^{\frac{5}{3} \cdot 3}}{9^{3} {(y^{\frac{8}{3}})}^{3}}$

Rewrite the expression.

$\frac{x^{5}}{9^{3} {(y^{\frac{8}{3}})}^{3}}$

Simplify the denominator.

Raise $9$ to the power of $3$ .

$\frac{x^{5}}{729 {(y^{\frac{8}{3}})}^{3}}$

Multiply the exponents in ${(y^{\frac{8}{3}})}^{3}$ .

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

$\frac{x^{5}}{729 y^{\frac{8}{3} \cdot 3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{x^{5}}{729 y^{\frac{8}{3} \cdot 3}}$

Rewrite the expression.

$\frac{x^{5}}{729 y^{8}}$

Simplify ((9x^(-2/3)y^(-1/3))/(xy^-3))^-3

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