Question

1. what is another way to write $x^{\frac{4}{3}}$?

$\sqrt4{x^3}$
$\frac{1}{4}x^3$
$\sqrt3{x^4}$
$\frac{1}{3}x^4$

Explanation:

Step1: Recall rational exponent rule

The rule for rational exponents is $x^{\frac{m}{n}} = \sqrt[n]{x^m}$ where $n$ is the root, $m$ is the power.

Step2: Match to given expression

For $x^{\frac{4}{3}}$, $m=4$, $n=3$. Substitute into the rule:
$x^{\frac{4}{3}} = \sqrt[3]{x^4}$

Answer:

$\boldsymbol{\sqrt[3]{x^4}}$ (the third option)