# How do you simplify (n^2 times n^3) /n^4?

Dec 24, 2016

$n$

#### Explanation:

First, we can simplify the numerator using the rule for exponents which states:

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

$\frac{{n}^{\textcolor{red}{2}} \times {n}^{\textcolor{b l u e}{3}}}{n} ^ 4 = {n}^{\textcolor{red}{2} + \textcolor{b l u e}{3}} / {n}^{4} = {n}^{5} / {n}^{4}$

Now, we can use another rule for exponents to simplify even further:

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

$\frac{{n}^{\textcolor{red}{5}}}{{n}^{\textcolor{b l u e}{4}}} = {x}^{\textcolor{red}{5} - \textcolor{b l u e}{4}} = {n}^{1}$

Finally, we can use one last rule for exponents to complete the simplification of this expression:

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

${n}^{1} = n$