Question

Use the law of exponents to rewrite and simplify the expression.

$\frac{1}{\sqrt[3]{x^4}}$

Answer 1

To simplify the given expression:

Using the law of exponents to simplify the given expression in below:

$\begin{array}{rcl}\frac{1}{\sqrt[3]{x^4}}& =& \frac{1}{x^{{\displaystyle \frac{4}{3}}}}\left[\text{Fraction exponent rule:}\sqrt[\text{n}]{{\text{a}}^{\text{m}}}={\text{a}}^{\frac{\text{m}}{\text{n}}}\right]\\ \therefore \frac{1}{\sqrt[3]{x^4}}& =& x^{-\frac{4}{3}}\left[\text{Negative exponent rule}:\frac{1}{{\text{a}}^{\text{m}}}=\left({\text{a}}^{\text{-m}}\right)\right]\end{array}$

Hence, the answer is $\begin{array}{l}{\mathit{x}}^{\mathbf{-}\frac{\mathbf{4}}{\mathbf{3}}}\end{array}$.