# How do you simplify q^-3divq^8?

Jan 3, 2017

See full simplification process below

#### Explanation:

First, we can rewrite this as:

${q}^{-} \frac{3}{q} ^ 8$

Now we can simplify using rules for exponents in two ways:

Simplification 1)

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

${q}^{\textcolor{red}{- 3}} / {q}^{\textcolor{b l u e}{8}} = {q}^{\textcolor{red}{- 3} - \textcolor{b l u e}{8}} =$

${q}^{-} 11$

Simplification 2)

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

${q}^{\textcolor{red}{- 3}} / {q}^{\textcolor{b l u e}{8}} = \frac{1}{q} ^ \left(\textcolor{b l u e}{8} - \textcolor{red}{- 3}\right) =$

$\frac{1}{q} ^ 11$