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^{(m)/(n)}=\sqrt[n]{a^m}`

Applying this rule to the case given:

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