# How do you simplify (1/4)^(1/2)?

Jan 29, 2017

$\pm \frac{1}{2}$

#### Explanation:

$\textcolor{b l u e}{\text{Demonstration of what this means using numbers}}$

${5}^{\frac{2}{3}} = \sqrt[3]{{5}^{2}}$

${5}^{\frac{9}{29}} = \sqrt[29]{{5}^{9}}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Answering the question}}$

Given:${\left(\frac{1}{4}\right)}^{\frac{1}{2}}$

This is the same as:$\text{ "root(2)((1/4)^1)" " ->" } \sqrt{{\left(\frac{1}{4}\right)}^{1}}$

Note that anything raised to the power of 1 is itself so ${\left(\frac{1}{4}\right)}^{1} = \frac{1}{4}$
so now we have: $\sqrt{\frac{1}{4}}$

This is the same as:$\text{ } \frac{\sqrt{1}}{\sqrt{4}} = \pm \frac{1}{2}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Footnote}}$

The answer has to be positive or negative.

$\left(- \frac{1}{2}\right) \times \left(- \frac{1}{2}\right) = + \frac{1}{4}$

$\left(+ \frac{1}{2}\right) \times \left(+ \frac{1}{2}\right) = + \frac{1}{4}$