# How do you simplify [ 3^2 / 3^ -1]^4?

Dec 22, 2016

${3}^{12}$

#### Explanation:

${\left[{3}^{2} / {3}^{-} 1\right]}^{4}$

first simplify the expression in brackets:

$\left[{3}^{2} / {3}^{-} 1\right]$

${a}^{m} / {a}^{n} = {a}^{m - n}$

using this law of indices:

$\left[{3}^{2} / {3}^{-} 1\right] = {3}^{2 - \left(- 1\right)} = {3}^{3}$

this simplifies the whole expression to ${\left({3}^{3}\right)}^{4}$

${\left({a}^{m}\right)}^{n} = {a}^{m \cdot n}$

using this law of indices:

${\left({3}^{3}\right)}^{4} = {3}^{3 \cdot 4} = {3}^{12}$