How do you simplify the expression (5g^4h^-3)^-3 using the properties?

Mar 2, 2017

See the entire simplification process below:

Explanation:

First, use these rules of exponents to simplify the outer exponent:

$x = {x}^{\textcolor{red}{1}}$ and ${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

${\left(5 {g}^{4} {h}^{-} 3\right)}^{-} 3 = {\left({5}^{\textcolor{red}{1}} {g}^{\textcolor{red}{4}} {h}^{\textcolor{red}{- 3}}\right)}^{\textcolor{b l u e}{- 3}} = {5}^{\textcolor{red}{1} \times \textcolor{b l u e}{- 3}} {g}^{\textcolor{red}{4} \times \textcolor{b l u e}{- 3}} {h}^{\textcolor{red}{- 3} \times \textcolor{b l u e}{- 3}} =$

${5}^{-} 3 {g}^{-} 12 {h}^{9}$

To simplify this for expression with no negative exponents use the following rule of exponents:

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

${5}^{\textcolor{red}{- 3}} {g}^{\textcolor{red}{- 12}} {h}^{9} = {h}^{9} / \left({5}^{\textcolor{red}{- - 3}} {g}^{\textcolor{red}{- - 12}}\right) = {h}^{9} / \left({5}^{3} {g}^{12}\right) = {h}^{9} / \left(125 {g}^{12}\right)$