# How do you simplify (c^8d^-12)/(c^-4d^-8)?

Jan 16, 2017

See the entire simplification process below:

#### Explanation:

To simplify this expression we will use this rule of exponents:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$

$\frac{{c}^{\textcolor{red}{8}} {d}^{\textcolor{red}{- 12}}}{{c}^{\textcolor{b l u e}{- 4}} {d}^{\textcolor{b l u e}{- 8}}} \to {c}^{\textcolor{red}{8} - \textcolor{b l u e}{- 4}} {d}^{\textcolor{red}{- 12} - \textcolor{b l u e}{- 8}} \to {c}^{\textcolor{red}{8} + \textcolor{b l u e}{4}} {d}^{\textcolor{red}{- 12} + \textcolor{b l u e}{8}} \to {c}^{12} {d}^{-} 4$

If we want to have only positive exponents we can use this rule of exponents:

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

${c}^{12} {d}^{\textcolor{red}{- 4}} \to {c}^{12} / {d}^{\textcolor{red}{4}} \to {c}^{12} / {d}^{4}$