# How do you simplify (32n^2p)/(2n^4p) and what are the ecluded values fot he variables?

Mar 30, 2017

#### Answer:

See the entire solution process below:

#### Explanation:

First, rewrite this expression as:

$\left(\frac{32}{2}\right) \left({n}^{2} / {n}^{4}\right) \left(\frac{p}{p}\right) = 16 \times {n}^{2} / {n}^{4} \times 1 = 16 \left({n}^{2} / {n}^{4}\right)$

Now, use this rule of exponents to simplify the $n$ terms:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = \frac{1}{x} ^ \left(\textcolor{b l u e}{b} - \textcolor{red}{a}\right)$

$16 \left({n}^{\textcolor{red}{2}} / {n}^{\textcolor{b l u e}{4 b}}\right) = 16 \left(\frac{1}{n} ^ \left(\textcolor{b l u e}{4} - \textcolor{red}{2}\right)\right) = 16 \left(\frac{1}{n} ^ 2\right) = \frac{16}{n} ^ 2$

From the original expression we cannot divide by $0$, therefore the excluded values are:

$2 {n}^{4} p$ cannot equal $0$ or $n \ne 0$ and $p \ne 0$