# How do you simplify sqrt(36 a^2 b^-8)?

Jan 8, 2017

Convert out of radical form and solve using the rules for exponents. See the full explanation below:

#### Explanation:

First we can rewrite this expression from radical form into exponent form:

$\sqrt{36 {a}^{2} {b}^{-} 8} = {\left(36 {a}^{2} {b}^{-} 8\right)}^{\frac{1}{2}}$

Next we can use this rule for exponents to simplify the parenthesis term:

${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

${36}^{\frac{1}{2}} {a}^{2 \times \frac{1}{2}} {b}^{- 8 \times \frac{1}{2}}$

$6 {a}^{1} {b}^{- 4}$

We can now use two other rules for exponents to finalize the simplification:

${x}^{\textcolor{red}{1}} = x$

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

$\frac{6 a}{b} ^ \left(- \left(- 4\right)\right)$

$\frac{6 a}{b} ^ 4$