# How do you simplify (2x^-2y^5 )/ (5y^5)?

May 29, 2018

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\frac{2}{5} \cdot {x}^{-} 2 \cdot {y}^{5} / {y}^{5} \implies$

$\frac{2}{5} \cdot {x}^{-} 2 \cdot 1 \implies$

$\frac{2}{5} \cdot {x}^{-} 2$

Next, use this rule for exponents to eliminate the negative exponent:

${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$

$\frac{2}{5} \cdot {x}^{\textcolor{red}{- 2}} \implies$

$\frac{2}{5} \cdot \frac{1}{x} ^ \textcolor{red}{- - 2} \implies$

$\frac{2}{5} \cdot {x}^{\textcolor{red}{- 2}} \implies$

$\frac{2}{5} \cdot \frac{1}{x} ^ \textcolor{red}{2} \implies$

$\frac{2}{5 {x}^{2}}$