Question

Try to evaluate (−64)4/3 without using a calculator. Enter DNE if the number is not real

Answer 1

Rational exponent rule

$a^{\frac{m}{n}}=\sqrt[n]{a^m}$

Applying this rule to the case given:

$\begin{gathered} (-64)^{\frac{4}{3}}=\sqrt[3]{(-64)^4}= \\ \text{ Evaluating inside the cubic root:} \\ =\sqrt[3]{16777216} \\ =256 \end{gathered}$