How do you simplify y^-3x^5*y^5x^-3?

Jun 3, 2018

Answer:

See a solution process below:

Explanation:

First, rewrite the expression as:

${x}^{5} \cdot {x}^{-} 3 \cdot {y}^{-} 3 \cdot {y}^{5} \implies$

$\left({x}^{5} \cdot {x}^{-} 3\right) \left({y}^{-} 3 \cdot {y}^{5}\right)$

Next, use this rule for exponents to simplify the $x$ and $y$ terms:

${z}^{\textcolor{red}{a}} \times {z}^{\textcolor{b l u e}{b}} = {z}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

$\left({x}^{\textcolor{red}{5}} \times {x}^{\textcolor{b l u e}{- 3}}\right) \left({y}^{\textcolor{red}{- 3}} \times {y}^{\textcolor{b l u e}{5}}\right) \implies$

${x}^{\textcolor{red}{5} + \textcolor{b l u e}{- 3}} {y}^{\textcolor{red}{- 3} + \textcolor{b l u e}{5}} \implies$

${x}^{\textcolor{red}{5} - \textcolor{b l u e}{3}} {y}^{\textcolor{red}{- 3} + \textcolor{b l u e}{5}} \implies$

${x}^{2} {y}^{2}$

Jun 3, 2018

Answer:

${x}^{2} {y}^{2}$

Explanation:

${y}^{-} 3 {x}^{5} \cdot {y}^{5} {x}^{-} 3$

Collecting like terms..

${y}^{-} 3 \cdot {y}^{5} \cdot {x}^{5} \cdot {x}^{-} 3$

${y}^{- 3 + 5} \cdot {x}^{5 + \left(- 3\right)}$

${y}^{2} \cdot {x}^{5 - 3}$

${y}^{2} \cdot {x}^{2}$

${x}^{2} {y}^{2}$