# How do you simplify (f^-3g^5h^8)^-3 and write it using only positive exponents?

Feb 21, 2017

See the entire simplification process below:

#### Explanation:

First use this rule of exponents to remove the exponent outside the parenthesis:

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

${\left({f}^{\textcolor{red}{- 3}} {g}^{\textcolor{red}{5}} {h}^{\textcolor{red}{8}}\right)}^{\textcolor{b l u e}{- 3}} = {f}^{\textcolor{red}{- 3} \times \textcolor{b l u e}{- 3}} {g}^{\textcolor{red}{5} \times \textcolor{b l u e}{- 3}} {h}^{\textcolor{red}{8} \times \textcolor{b l u e}{- 3}} = {f}^{9} {g}^{- 15} {h}^{- 24}$

Now, we can use this rule of exponents to remove the negative exponents:
${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$

${f}^{9} {g}^{\textcolor{red}{- 15}} {h}^{\textcolor{red}{- 24}} = {f}^{9} / {g}^{\textcolor{red}{- - 15}} {h}^{\textcolor{red}{- - 24}} = {f}^{9} / {g}^{15} {h}^{24}$