# How do you simplify (2xy^4)/(-x^2 y^0)?

Mar 10, 2018

See a solution process below:

#### Explanation:

First, use this rule of exponents to simplify the denominator:

${a}^{\textcolor{red}{0}} = 1$

$\frac{2 x {y}^{4}}{- {x}^{2} {y}^{\textcolor{red}{0}}} \implies \frac{2 x {y}^{4}}{- {x}^{2} \times 1} \implies \frac{2 x {y}^{4}}{- {x}^{2}} \implies - \frac{2 x {y}^{4}}{x} ^ 2$

Next, use these rules for exponents to simplify the $x$ terms:

$a = {a}^{\textcolor{red}{1}}$ and ${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = \frac{1}{x} ^ \left(\textcolor{b l u e}{b} - \textcolor{red}{a}\right)$ and ${a}^{\textcolor{red}{1}} = a$

$- \frac{2 x {y}^{4}}{x} ^ 2 \implies - \frac{2 {x}^{\textcolor{red}{1}} {y}^{4}}{x} ^ \textcolor{b l u e}{2} \implies - \frac{2 {y}^{4}}{x} ^ \left(\textcolor{b l u e}{2} - \textcolor{red}{1}\right) \implies - \frac{2 {y}^{4}}{x} ^ \textcolor{red}{1} \implies - \frac{2 {y}^{4}}{x}$