# How do you simplify 192^(1/6)?

Aug 13, 2017

See a solution process below:

#### Explanation:

First, we can rewrite the expression as:

${\left(64 \cdot 3\right)}^{\frac{1}{6}} \implies {\left({2}^{6} \cdot 3\right)}^{\frac{1}{6}} \implies {\left({2}^{6}\right)}^{\frac{1}{6}} \cdot {3}^{\frac{1}{6}}$

We can use these rules of exponents to simplify the $2 \text{'s}$ term:

${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$ and ${a}^{\textcolor{red}{1}} = a$

${\left({2}^{\textcolor{red}{6}}\right)}^{\textcolor{b l u e}{\frac{1}{6}}} \cdot {3}^{\frac{1}{6}} \implies {2}^{\textcolor{red}{6} \times \textcolor{b l u e}{\frac{1}{6}}} \cdot {3}^{\frac{1}{6}} \implies {2}^{\textcolor{red}{1}} \cdot {3}^{\frac{1}{6}} \implies 2 \cdot {3}^{\frac{1}{6}}$

If necessary, we can write this in radical form using this rule for exponents:

${x}^{\frac{1}{\textcolor{red}{n}}} = \sqrt[\textcolor{red}{n}]{x}$

$2 \cdot {3}^{\frac{1}{\textcolor{red}{6}}} = 2 \sqrt[\textcolor{red}{6}]{3}$