# How do you simplify ((3x^7)/(2y^12))^4 and write it using only positive exponents?

##### 1 Answer
Jun 11, 2017

See a solution process below:

#### Explanation:

Use, these rules of exponents to simplify the expression:

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

${\left(\frac{3 {x}^{7}}{2 {y}^{12}}\right)}^{4} \implies {\left(\frac{{3}^{\textcolor{red}{1}} {x}^{\textcolor{red}{7}}}{{2}^{\textcolor{red}{1}} {y}^{\textcolor{red}{12}}}\right)}^{\textcolor{b l u e}{4}} \implies \frac{{3}^{\textcolor{red}{1} \times \textcolor{b l u e}{4}} {x}^{\textcolor{red}{7} \times \textcolor{b l u e}{4}}}{{2}^{\textcolor{red}{1} \times \textcolor{b l u e}{4}} {y}^{\textcolor{red}{12} \times \textcolor{b l u e}{4}}} \implies \frac{{3}^{4} {x}^{28}}{{2}^{4} {y}^{48}} \implies$

$\frac{81 {x}^{28}}{16 {y}^{48}}$