# How do you simplify (45mn^3) /( 20n^7)?

Jul 29, 2015

You cancel terms that are common to the numerator and denominator.

#### Explanation:

Your initial expression looks like this

$\frac{45 m {n}^{3}}{20 {n}^{7}}$

You can simplify this expression by using the product of powers property of exponents

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

to rewrite ${n}^{7}$ as

${n}^{7} = {n}^{3} \cdot {n}^{4}$

$\frac{45 m {n}^{3}}{20 {n}^{7}} = \frac{45 \cdot m \cdot {n}^{3}}{20 \cdot {n}^{3} \cdot {n}^{4}} = \frac{5 \cdot 9 \cdot m \cdot {n}^{3}}{5 \cdot 4 \cdot {n}^{3} \cdot {n}^{4}}$
$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} \cdot 9 \cdot m \cdot \textcolor{p u r p \le}{\cancel{\textcolor{b l a c k}{{n}^{3}}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} \cdot 4 \cdot \textcolor{p u r p \le}{\cancel{\textcolor{b l a c k}{{n}^{3}}}} \cdot {n}^{4}} = \textcolor{g r e e n}{\frac{9 \cdot m}{4 \cdot {n}^{4}}}$
$\frac{9 \cdot m}{2 {n}^{2}} ^ 2$