How do you write $7^{\frac{3}{4}}$ $7^(3/4)$ in radical form?

Question

10710 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-15T01:24:19

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

$7^{\frac{3}{4}}$ $7^(3/4)$

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 $7^{\frac{3}{4}}$ $7^(color(red)3/4)$ , the numerator $3$ $color(red)3$ is the "power" or exponent of the final expression.

The denominator $4$ $color(blue)4$ in $7^{\frac{3}{4}}$ $7^(3/color(blue)4$ is the root.

${(\sqrt[4]{7})}^{3}$ $(root(color(blue)4)7)^color(red)3$

This can also be written as $\sqrt[4]{7^{3}}$ $root(color(blue)4)(7^color(red)3)$

How do you write 7347^(3/4) in radical form?