# How do you simplify ((2c^3d^5)/(5g^2))^5?

Mar 18, 2017

See the entire solution process below:

#### Explanation:

First, use this rule of exponents to rewrite the constants in the expression: $a = {a}^{\textcolor{red}{1}}$

$\frac{{2}^{\textcolor{red}{1}} {c}^{3} {d}^{5}}{{5}^{\textcolor{red}{1}} {g}^{2}}$

Next, use this rule of exponents to eliminate the outer exponent:

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

${\left(\frac{{2}^{\textcolor{red}{1}} {c}^{\textcolor{red}{3}} {d}^{\textcolor{red}{5}}}{{5}^{\textcolor{red}{1}} {g}^{\textcolor{red}{2}}}\right)}^{\textcolor{b l u e}{5}} = \frac{{2}^{\textcolor{red}{1} \times \textcolor{b l u e}{5}} {c}^{\textcolor{red}{3} \times \textcolor{b l u e}{5}} {d}^{\textcolor{red}{5} \times \textcolor{b l u e}{5}}}{{5}^{\textcolor{red}{1} \times \textcolor{b l u e}{5}} {g}^{\textcolor{red}{2} \times \textcolor{b l u e}{5}}} = \frac{{2}^{5} {c}^{15} {d}^{25}}{{5}^{5} {g}^{10}}$

If we expand the constants the result is:

$\frac{32 {c}^{15} {d}^{25}}{3125 {g}^{10}}$