What is a^(1/2)b^(4/3)c^(3/4) in radical form?

Jul 20, 2017

See a solution process below:

Explanation:

First, rewrite the expression as:

${a}^{\frac{1}{2}} {b}^{4 \times \frac{1}{3}} {c}^{3 \times \frac{1}{4}}$

We can then use this rule of exponents to rewrite the $b$ and $c$ terms:

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

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

We can now use rule to write this in radical form:

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

$\sqrt[2]{a} \sqrt[3]{{b}^{4}} \sqrt[4]{{c}^{3}}$

Or

$\sqrt{a} \sqrt[3]{{b}^{4}} \sqrt[4]{{c}^{3}}$