Question

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

$8^{\frac{4}{3}}$

Answer 1

Simplify the expression:

Consider the given expression.

$\begin{array}{rcl}{8}^{\frac{4}{3}}& =& {\left(8^{\frac{1}{3}}\right)}^4\end{array}$

Using the exponent property $\begin{array}{rcl}{\left(a^m\right)}^n& =& a^{mn}\end{array}$,

$\begin{array}{rcl}{8}^{\frac{4}{3}}& =& {\left(8^{\frac{1}{3}}\right)}^4\\ & \Rightarrow & 8^{\frac{4}{3}}={\left(2\right)}^4\\ & \Rightarrow & 8^{\frac{4}{3}}=16\end{array}$

Hence, the simplified expression is $\mathbf{16}$.