How do you simplify (\frac { - x ^ { 4} y ^ { 4} \cdot - x ^ { - 2} y ^ { 3} } { - x y ^ { - 1} } ) ^ { 4}?

Jul 24, 2018

${x}^{4} {y}^{32}$

Explanation:

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

Numerator:
$- {x}^{4} {y}^{4} \cdot - {x}^{- 2} {y}^{3}$
=$- {x}^{4} {y}^{4} \times - {y}^{3} / {x}^{2}$
=${x}^{2} {y}^{7}$

Denominator:
$- x {y}^{- 1}$
=$- \frac{x}{y}$

Therefore,
${\left(\frac{- {x}^{4} {y}^{4} \cdot - {x}^{- 2} {y}^{3}}{- x {y}^{- 1}}\right)}^{4}$ becomes ${\left(\frac{{x}^{2} {y}^{7}}{- \frac{x}{y}}\right)}^{4}$
=${\left(\left({x}^{2} {y}^{7}\right) \times - \frac{y}{x}\right)}^{4}$
=${\left(- x {y}^{8}\right)}^{4}$
=${x}^{4} {y}^{32}$