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

Jul 13, 2015

${\left(\frac{2 m}{n} ^ 2\right)}^{4} = \frac{16 {m}^{4}}{n} ^ 8$

You must apply the outside exponent to everything inside the parentheses.

${\left(\frac{2 m}{n} ^ 2\right)}^{4} = \frac{{2}^{4} {m}^{4}}{{n}^{2}} ^ 4$

We have to repeat the procedure with the denominator.

$\frac{{2}^{4} {m}^{4}}{{n}^{2}} ^ 4 = \frac{{2}^{4} {m}^{4}}{n} ^ 8$

So

${\left(\frac{2 m}{n} ^ 2\right)}^{4} = \frac{{2}^{4} {m}^{4}}{n} ^ 8 = \frac{16 {m}^{4}}{n} ^ 8$

Jul 13, 2015

The answer is $\frac{16 {m}^{4}}{n} ^ 8$.

#### Explanation:

${\left(\frac{2 m}{{n}^{2}}\right)}^{4}$

${\left(\frac{a}{b}\right)}^{x} = \frac{{a}^{x}}{{b}^{x}}$

${\left(2 m\right)}^{4} / {\left({n}^{2}\right)}^{4}$

${\left({a}^{x}\right)}^{y} = {a}^{x \cdot y}$

(2m)^4/(n^(2*4) =

${\left(2 m\right)}^{4} / {n}^{8}$

${\left(a b\right)}^{x} = {a}^{x} {b}^{y}$

$\frac{{2}^{4} {m}^{4}}{n} ^ 8$ =

$\frac{16 {m}^{4}}{n} ^ 8$