# How do you simplify ((p+1)(2p-1)^4)/((p+1)^2(2p-1)^2)?

Apr 15, 2017

$\frac{{\left(2 p - 1\right)}^{2}}{\left(p + 1\right)}$

#### Explanation:

This is just a question of knowing your indice laws.

$\frac{\left(p + 1\right) {\left(2 p - 1\right)}^{4}}{{\left(p + 1\right)}^{2} {\left(2 p - 1\right)}^{2}}$

When there is a division of indices with the same base, the indices are subtracted.

For $\left(p + 1\right)$, it is $1 - 2 = - 1$, therefore the (p+1) on the numerator disappears and the one on the denominator stays.

$\frac{{\left(2 p - 1\right)}^{4}}{\left(p + 1\right) {\left(2 p - 1\right)}^{2}}$

For $\left(2 p - 1\right)$, it is $4 - 2 = 2$, therefore the $\left(2 p - 1\right)$ on the denominator disappears and the one on the numerator stays.

$\frac{{\left(2 p - 1\right)}^{2}}{\left(p + 1\right)}$