How do you simplify ((3m^5r^3)/(4p^8))^4?

May 18, 2017

See a solution process below:

Explanation:

First, use this rule of exponents to rewrite the expression:

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

${\left(\frac{3 {m}^{5} {r}^{3}}{4 {p}^{8}}\right)}^{4} \implies {\left(\frac{{3}^{\textcolor{red}{1}} {m}^{5} {r}^{3}}{{4}^{\textcolor{red}{1}} {p}^{8}}\right)}^{4}$

Next, use this rule of equations to complete the simplification:

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

${\left(\frac{{3}^{\textcolor{red}{1}} {m}^{5} {r}^{3}}{{4}^{\textcolor{red}{1}} {p}^{8}}\right)}^{4} \implies {\left(\frac{{3}^{\textcolor{red}{1}} {m}^{\textcolor{red}{5}} {r}^{\textcolor{red}{3}}}{{4}^{\textcolor{red}{1}} {p}^{\textcolor{red}{8}}}\right)}^{\textcolor{b l u e}{4}} \implies \frac{{3}^{\textcolor{red}{1} \times \textcolor{b l u e}{4}} {m}^{\textcolor{red}{5} \times \textcolor{b l u e}{4}} {r}^{\textcolor{red}{3} \times \textcolor{b l u e}{4}}}{{4}^{\textcolor{red}{1} \times \textcolor{b l u e}{4}} {p}^{\textcolor{red}{8} \times \textcolor{b l u e}{4}}} \implies$

$\frac{{3}^{4} {m}^{20} {r}^{12}}{{4}^{4} {p}^{32}} \implies \frac{81 {m}^{20} {r}^{12}}{256 {p}^{32}}$