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

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

Step 1

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

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

Step 2

Multiply $y$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

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

Multiply $y^{3}$ by $y$ .

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

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

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

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

Add $3$ and $1$ .

${(\frac{x^{3}}{x^{2} y^{4}})}^{- 3}$

Step 3

Cancel the common factor of $x^{3}$ and $x^{2}$ .

Factor $x^{2}$ out of $x^{3}$ .

${(\frac{x^{2} x}{x^{2} y^{4}})}^{- 3}$

Cancel the common factors.

Factor $x^{2}$ out of $x^{2} y^{4}$ .

${(\frac{x^{2} x}{x^{2} (y^{4})})}^{- 3}$

Cancel the common factor.

${(\frac{x^{2} x}{x^{2} y^{4}})}^{- 3}$

Rewrite the expression.

${(\frac{x}{y^{4}})}^{- 3}$

Step 4

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

${(\frac{y^{4}}{x})}^{3}$

Step 5

Apply the product rule to $\frac{y^{4}}{x}$ .

$\frac{{(y^{4})}^{3}}{x^{3}}$

Step 6

Multiply the exponents in ${(y^{4})}^{3}$ .

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

$\frac{y^{4 \cdot 3}}{x^{3}}$

Multiply $4$ by $3$ .

$\frac{y^{12}}{x^{3}}$