Simplify (-xy)^4*(-3x^-2)^3

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

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

Apply the product rule to $- x y$ .

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

Apply the product rule to $- x$ .

${(- 1)}^{4} x^{4} y^{4} \cdot {(- 3 x^{- 2})}^{3}$

Raise $- 1$ to the power of $4$ .

$1 x^{4} y^{4} \cdot {(- 3 x^{- 2})}^{3}$

Multiply $x^{4}$ by $1$ .

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

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

$x^{4} y^{4} \cdot {(- 3 \frac{1}{x^{2}})}^{3}$

Combine $- 3$ and $\frac{1}{x^{2}}$ .

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

Move the negative in front of the fraction.

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

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

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

$x^{4} y^{4} \cdot ({(- 1)}^{3} {(\frac{3}{x^{2}})}^{3})$

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

$x^{4} y^{4} \cdot ({(- 1)}^{3} \frac{3^{3}}{{(x^{2})}^{3}})$

Simplify the expression.

Rewrite using the commutative property of multiplication.

${(- 1)}^{3} x^{4} y^{4} \frac{3^{3}}{{(x^{2})}^{3}}$

Raise $- 1$ to the power of $3$ .

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

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

$- x^{4} y^{4} \frac{27}{{(x^{2})}^{3}}$

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

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

$- x^{4} y^{4} \frac{27}{x^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$- x^{4} y^{4} \frac{27}{x^{6}}$

Cancel the common factor of $x^{4}$ .

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

$x^{4} (- y^{4}) \frac{27}{x^{6}}$

Factor $x^{4}$ out of $x^{6}$ .

$x^{4} (- y^{4}) \frac{27}{x^{4} x^{2}}$

Cancel the common factor.

$x^{4} (- y^{4}) \frac{27}{x^{4} x^{2}}$

Rewrite the expression.

$- y^{4} \frac{27}{x^{2}}$

Combine $\frac{27}{x^{2}}$ and $y^{4}$ .

$- \frac{27 y^{4}}{x^{2}}$