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

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

Step 1

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

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

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

Cancel the common factors.

Factor $x$ out of $3 x y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

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

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

Cancel the common factors.

Factor $y$ out of $3 y$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

Step 4

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

Apply the product rule to $\frac{3}{2 x^{2} y}$ .

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

Apply the product rule to $2 x^{2} y$ .

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

Apply the product rule to $2 x^{2}$ .

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

Step 5

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

$\frac{27}{2^{3} {(x^{2})}^{3} y^{3}}$

Step 6

Simplify the denominator.

Raise $2$ to the power of $3$ .

$\frac{27}{8 {(x^{2})}^{3} y^{3}}$

Multiply the exponents in ${(x^{2})}^{3}$ .

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

$\frac{27}{8 x^{2 \cdot 3} y^{3}}$

Multiply $2$ by $3$ .

$\frac{27}{8 x^{6} y^{3}}$

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

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