# Question b7a06

Jan 9, 2018

See a solution process below"

#### Explanation:

Assuming you are looking for the radical form of ${4}^{\frac{2}{3}}$

We can rewrite the expression as:

${4}^{2 \times \frac{1}{3}}$

We can use this rule for exponents to simplify the expression giving:

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

${4}^{\textcolor{red}{2} \times \textcolor{b l u e}{\frac{1}{3}}} \implies {\left({4}^{\textcolor{red}{2}}\right)}^{\textcolor{b l u e}{\frac{1}{3}}} \implies {16}^{\frac{1}{3}}$

We can now use this rule for exponents to write the expression in radical form:

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

${16}^{\frac{1}{\textcolor{red}{3}}} \implies \sqrt[\textcolor{red}{3}]{16}$

If necessary, we can use this rule for radicals to simplify the expression:

$\sqrt[n]{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}} = \sqrt[n]{\textcolor{red}{a}} \cdot \sqrt[n]{\textcolor{b l u e}{b}}$

$\sqrt[3]{16} \implies \sqrt[3]{\textcolor{red}{8} \cdot \textcolor{b l u e}{2}} \implies \sqrt[3]{\textcolor{red}{8}} \cdot \sqrt[3]{\textcolor{b l u e}{2}} \implies 2 \sqrt[3]{2}$

Jan 9, 2018

$2 \sqrt[3]{2}$

#### Explanation:

color(blue)(4^(2/3)

We can simplify this using the law of exponents

color(brown)(x^(y/z)=root(z)(x^y)

So,

$\rightarrow {4}^{\frac{2}{3}} = \sqrt[3]{{4}^{2}}$

color(green)(rArrroot(3)(16)$=$color (red)(root (3)(2×2^3)#
$\textcolor{b l u e}{2 \sqrt[3]{2}}$
Hope this helps!!! ☺☻