# What is (14x^3y^6)/(7x^5y^2)?

Feb 28, 2016

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

#### Explanation:

$1$. Factor out $7$ from the numerator and denominator.

$\frac{14 {x}^{3} {y}^{6}}{7 {x}^{5} {y}^{2}}$

$= \frac{7 \left(2 {x}^{3} {y}^{6}\right)}{7 \left({x}^{5} {y}^{2}\right)}$

$2$. Simplify.

$= \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} \left(2 {x}^{3} {y}^{6}\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}} \left({x}^{5} {y}^{2}\right)}$

$= \frac{2 {x}^{3} {y}^{6}}{{x}^{5} {y}^{2}}$

$3$. Factor out ${x}^{3}$ from the numerator and denominator. Recall the exponent quotient rule: ${a}^{m} \div {a}^{n} = {a}^{m - n}$.

$= \frac{{x}^{3} \left(2 {y}^{6}\right)}{{x}^{3} \left({x}^{2} {y}^{2}\right)}$

$4$. Simplify.

$= \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{{x}^{3}}}} \left(2 {y}^{6}\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{{x}^{3}}}} \left({x}^{2} {y}^{2}\right)}$

$= \frac{2 {y}^{6}}{{x}^{2} {y}^{2}}$

$5$. Factor out ${y}^{2}$ from the numerator and denominator.

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

$6$. Simplify.

$= \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{{y}^{2}}}} \left(2 {y}^{4}\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{{y}^{2}}}} \left({x}^{2}\right)}$

$7$. Rewrite the expression.

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

$\therefore$, the simplified expression is $\frac{2 {y}^{4}}{{x}^{2}}$.