# How do you simplify the expression (108a^8)/(12a^4b^3)?

Aug 18, 2017

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\frac{108}{12} \left({a}^{8} / {a}^{4}\right) \left(\frac{1}{b} ^ 3\right) \implies 9 \left({a}^{8} / {a}^{4}\right) \left(\frac{1}{b} ^ 3\right) \implies \frac{9}{b} ^ 3 \left({a}^{8} / {a}^{4}\right)$

We can now use this rule for exponents to simplify the $a$ terms:

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

$\frac{9}{b} ^ 3 \left({a}^{\textcolor{red}{8}} / {a}^{\textcolor{b l u e}{4}}\right) \implies \frac{9}{b} ^ 3 {a}^{\textcolor{red}{8} - \textcolor{b l u e}{4}} \implies \frac{9 {a}^{4}}{b} ^ 3$