How do you write 7^(3/4) in radical form?

Oct 15, 2016

${\left(\sqrt[4]{7}\right)}^{3}$ or root(4)(7^3

Explanation:

${7}^{\frac{3}{4}}$

The numerator of the rational exponent represents the "power".
The denominator represents the "root".

A trick to remembering this is the saying "higher power" for the numerator and "the roots of a plant are at the bottom" for the denominator.

In this example ${7}^{\frac{\textcolor{red}{3}}{4}}$, the numerator $\textcolor{red}{3}$ is the "power" or exponent of the final expression.

The denominator $\textcolor{b l u e}{4}$ in 7^(3/color(blue)4 is the root.

${\left(\sqrt[\textcolor{b l u e}{4}]{7}\right)}^{\textcolor{red}{3}}$

This can also be written as $\sqrt[\textcolor{b l u e}{4}]{{7}^{\textcolor{red}{3}}}$