# How do you simplify [x^-9(81x^8)]^(5/4)?

Apr 25, 2017

$= \frac{243}{{x}^{\frac{5}{4}}} = \frac{243}{{\sqrt[4]{x}}^{5}}$

#### Explanation:

Use the power law of indices - multiply the indices.

${\left[{x}^{-} 9 \left(81 {x}^{8}\right)\right]}^{\frac{5}{4}} \text{ = } {x}^{- \frac{45}{4}} \times {81}^{\frac{5}{4}} {x}^{10}$

Recall: $\textcolor{red}{{x}^{m} \times {x}^{n} = {x}^{m + n}} \text{ and } \textcolor{b l u e}{{x}^{\frac{p}{q}} = {\sqrt[q]{x}}^{p}}$

$\textcolor{red}{{x}^{- \frac{45}{4}}} \times \textcolor{b l u e}{{81}^{\frac{5}{4}}} \textcolor{red}{{x}^{10}} = \textcolor{b l u e}{{\sqrt[4]{81}}^{5}} \textcolor{red}{{x}^{- \frac{5}{4}}}$

Recall: ${x}^{-} m = \frac{1}{x} ^ m$

$= \frac{\textcolor{b l u e}{{3}^{5}}}{\textcolor{red}{{x}^{\frac{5}{4}}}}$

$= \frac{243}{{x}^{\frac{5}{4}}}$