# How do you simplify \frac{3x^{2} y^{2}}{4x y^{4}}?

Apr 27, 2017

See a solution process below:

#### Explanation:

First, rewrite this expression as:

$\frac{3}{4} \left({x}^{2} / x\right) \left({y}^{2} / {y}^{4}\right)$

Next, use these three rules of exponents to begin the simplification process:

$a = {a}^{\textcolor{b l u e}{1}}$ and ${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$ and ${x}^{\textcolor{g r e e n}{a}} / {x}^{\textcolor{p u r p \le}{b}} = \frac{1}{x} ^ \left(\textcolor{p u r p \le}{b} - \textcolor{g r e e n}{a}\right)$

$\frac{3}{4} \left({x}^{2} / x\right) \left({y}^{2} / {y}^{4}\right) = \frac{3}{4} \left({x}^{\textcolor{red}{2}} / {x}^{\textcolor{b l u e}{1}}\right) \left({y}^{\textcolor{g r e e n}{2}} / {y}^{\textcolor{p u r p \le}{4}}\right) = \frac{3}{4} \left({x}^{\textcolor{red}{2} - \textcolor{b l u e}{1}}\right) \left(\frac{1}{y} ^ \left(\textcolor{p u r p \le}{4} - \textcolor{g r e e n}{2}\right)\right) =$

$\frac{3}{4} \left({x}^{1}\right) \left(\frac{1}{y} ^ 2\right) = \frac{3 {x}^{1}}{4 {y}^{2}}$

Now, use this rule of exponents (the reverse of the first rule used above) to complete the simplification:

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

$\frac{3 {x}^{\textcolor{red}{1}}}{4 {y}^{2}} = \frac{3 x}{4 {y}^{2}}$

Apr 27, 2017

$\frac{3 x}{4 {y}^{2}}$

#### Explanation:

color(blue)((3x^2y^2)/(4xy^4)

Cancel the variables

$\rightarrow \frac{3 \cancel{{x}^{2}} {y}^{2}}{4 \cancel{x} {y}^{4}}$

$\rightarrow \frac{3 x {y}^{2}}{4 {y}^{4}}$

rarr(3xcancel(y^2))/(4cancel(y^4)

color(green)(rArr(3x)/(4y^2)

Hope this helps!.. :)