# How do you simplify (28x^-2)/(7y^-3) and write it using only positive exponents?

Aug 4, 2017

See a solution process below:

#### Explanation:

First, simplify the constants:

$\frac{\left(7 \times 4\right) {x}^{-} 2}{7 {y}^{-} 3} \implies$

$\frac{\left(\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} \times 4\right) {x}^{-} 2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} {y}^{-} 3} \implies$

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

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

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

$\frac{4 {x}^{-} 2}{y} ^ \textcolor{red}{- 3} \implies$

$4 {x}^{-} 2 {y}^{\textcolor{red}{3}}$

Now, use this rule of exponents to eliminate the negative exponent for $x$:

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

$4 {x}^{\textcolor{red}{- 2}} {y}^{3} \implies$

$\frac{4 {y}^{3}}{x} ^ \textcolor{red}{- - 2} \implies$

$\frac{4 {y}^{3}}{x} ^ \textcolor{red}{2}$