Question

(64)^{\frac{2}{3}}

Explanation:

Step1: Recall exponent rules

We know that \(a^{\frac{m}{n}}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m\). For \((64)^{\frac{2}{3}}\), we can use this rule. First, find the cube root of 64.

Step2: Calculate the cube root of 64

The cube root of 64, \(\sqrt[3]{64}\), since \(4\times4\times4 = 64\), so \(\sqrt[3]{64}=4\).

Step3: Square the result

Now we have \((\sqrt[3]{64})^2 = 4^2\). And \(4^2 = 16\).

Answer:

16