How do you simplify (3r^7)/(2r^2)^4?

Oct 29, 2016

$\frac{3}{16 r}$

Explanation:

This fraction is simplified by using the power identities of powers with same base

color(blue)((r^n)^m=r^(nxxm)

$\textcolor{red}{{r}^{m} / {r}^{n} = {r}^{m - n}}$

${\textcolor{p u r p \le}{\left(a \times b\right)}}^{m} = {a}^{m} \times {b}^{m}$

$\frac{3 {r}^{7}}{2 {r}^{2}} ^ 4 = \frac{3 {r}^{7}}{{2}^{4} \textcolor{b l u e}{{r}^{2 \times 4}}}$

$\frac{3 {r}^{7}}{2 {r}^{2}} ^ 4 = \frac{3 {r}^{7}}{{2}^{4} {r}^{8}}$

$\frac{3 {r}^{7}}{2 {r}^{2}} ^ 4 = \left(\frac{3}{2} ^ 4\right) \left({r}^{7} / {r}^{8}\right)$

$\frac{3 {r}^{7}}{2 {r}^{2}} ^ 4 = \left(\frac{3}{16}\right) \textcolor{red}{{r}^{7 - 8}}$

$\frac{3 {r}^{7}}{2 {r}^{2}} ^ 4 = \frac{3 {r}^{- 1}}{16}$

$\frac{3 {r}^{7}}{2 {r}^{2}} ^ 4 = \frac{3}{16 r}$