# Applying the laws of exponents, how do we simplify (16^(-1/2))^(-1/2) ?

Sep 12, 2017

$2$

#### Explanation:

$\text{using the "color(blue)"laws of exponents}$

•color(white)(x)(a^m)^n=a^(mn)

•color(white)(x)a^(m/n)=root(n)(a^m)

$\Rightarrow {\left({16}^{- \frac{1}{2}}\right)}^{- \frac{1}{2}} = {16}^{\left(\frac{1}{2} \times \frac{1}{2}\right)} = {16}^{\frac{1}{4}}$

$\Rightarrow {16}^{\frac{1}{4}} = \sqrt[4]{16} = 2$