# How do you simplify r^-2/(4r^5*4r^-5) and write it using only positive exponents?

May 8, 2017

$\frac{1}{16 {r}^{2}}$

#### Explanation:

Note that $\frac{1}{r} ^ - 5$ is the same as ${5}^{5}$ and ${r}^{- 2}$ is the same as $\frac{1}{r} ^ 2$

Splitting ${r}^{- 2} / \left(4 {r}^{5} \times 4 {r}^{- 5}\right)$ gives:

$\frac{1}{4} \times \frac{1}{4} \times {r}^{- 2} \times \frac{1}{r} ^ 5 \times \frac{1}{r} ^ \left(- 5\right)$

$\frac{1}{4} \times \frac{1}{4} \times \frac{1}{r} ^ 2 \times \frac{1}{r} ^ 5 \times {r}^{5}$

$\frac{1}{16} \times \frac{1}{r} ^ 2 \times {r}^{5} / {r}^{5}$

But ${r}^{5} / {r}^{5} = 1 \leftarrow$ This is the same thing as cancelling,

$\frac{1}{16} \times \frac{1}{r} ^ 2 = \frac{1}{16 {r}^{2}}$