# How do you change a^(1/2)b^(4/3)c^(3/4) into radical form?

May 20, 2017

See a solution process below:

#### Explanation:

First, we can use this rule of exponents to put the $a$ term into radical form:

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

${a}^{\frac{1}{\textcolor{red}{2}}} {b}^{\frac{4}{3}} {c}^{\frac{3}{4}} \implies \left(\sqrt[\textcolor{red}{2}]{a}\right) {b}^{\frac{4}{3}} {c}^{\frac{3}{4}} \implies \left(\sqrt{a}\right) {b}^{\frac{4}{3}} {c}^{\frac{3}{4}}$

Next, we can use this rule of exponents to rewrite the $b$ and $c$ terms:

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

$\left(\sqrt{a}\right) {b}^{\frac{4}{3}} {c}^{\frac{3}{4}} \implies \left(\sqrt{a}\right) {b}^{\textcolor{red}{4} \times \textcolor{b l u e 0}{\frac{1}{3}}} {c}^{\textcolor{red}{3} \times \textcolor{b l u e}{\frac{1}{4}}} \implies \sqrt{a} {\left({b}^{4}\right)}^{\frac{1}{3}} {\left({c}^{3}\right)}^{\frac{1}{4}}$

We can again use this rule of exponents to put the $b$ and $c$ terms in radical form:

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

$\sqrt{a} {\left({b}^{4}\right)}^{\frac{1}{\textcolor{red}{3}}} {\left({c}^{3}\right)}^{\frac{1}{\textcolor{red}{4}}} \implies \sqrt{a} \sqrt[\textcolor{red}{3}]{{b}^{4}} \sqrt[\textcolor{red}{4}]{{c}^{3}}$