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

Feb 10, 2017

First, rewrite the numerator and use this rule for exponents to simplify the numerator:

${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

$\frac{{x}^{\textcolor{red}{3}} \cdot {x}^{\textcolor{b l u e}{3}} \cdot {y}^{3}}{4 {x}^{2}} = \frac{{x}^{\textcolor{red}{3} + \textcolor{b l u e}{3}} \cdot {y}^{3}}{4 {x}^{2}} = \frac{{x}^{6} {y}^{3}}{4 {x}^{2}}$

Now, we can use this rule for exponents to simplify the $x$ terms in the numerator and denominator:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$

$\frac{{x}^{\textcolor{red}{6}} {y}^{3}}{4 {x}^{\textcolor{b l u e}{2}}} = \frac{{x}^{\textcolor{red}{6} - \textcolor{b l u e}{2}} {y}^{3}}{4} = \frac{{x}^{4} {y}^{3}}{4}$