Question

express $64^{\frac{2}{3}}$ in simplest radical form.

Explanation:

Step1: Recall exponent rule

The exponent rule for \(a^{\frac{m}{n}}\) is \(a^{\frac{m}{n}}=\sqrt[n]{a^{m}}\) or \((\sqrt[n]{a})^{m}\). For \(64^{\frac{2}{3}}\), we can use \((\sqrt[3]{64})^{2}\).

Step2: Find cube root of 64

We know that \(4\times4\times4 = 64\), so \(\sqrt[3]{64}=4\).

Step3: Square the result

Now, square the result from Step 2: \(4^{2}=16\).

Answer:

\(16\)