How do you simplify ((3xy^4)/(5z^2))^2?

May 13, 2017

See a solution process below:

Explanation:

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

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

${\left(\frac{3 x {y}^{4}}{5 {z}^{2}}\right)}^{2} \implies {\left(\frac{{3}^{\textcolor{red}{1}} {x}^{\textcolor{red}{1}} {y}^{4}}{{5}^{\textcolor{red}{1}} {z}^{2}}\right)}^{2}$

Now, use this rule of exponents to eliminate the exponent outside the parenthesis:

${\left(\frac{{3}^{\textcolor{red}{1}} {x}^{\textcolor{red}{1}} {y}^{\textcolor{red}{4}}}{{5}^{\textcolor{red}{1}} {z}^{\textcolor{red}{2}}}\right)}^{\textcolor{b l u e}{2}} \implies \frac{{3}^{\textcolor{red}{1} \times \textcolor{b l u e}{2}} {x}^{\textcolor{red}{1} \times \textcolor{b l u e}{2}} {y}^{\textcolor{red}{4} \times \textcolor{b l u e}{2}}}{{5}^{\textcolor{red}{1} \times \textcolor{b l u e}{2}} {z}^{\textcolor{red}{2} \times \textcolor{b l u e}{2}}} \implies \frac{{3}^{2} {x}^{2} {y}^{8}}{{5}^{2} {z}^{4}} \implies$

$\frac{9 {x}^{2} {y}^{8}}{25 {z}^{4}}$