Question

evaluate without a calculator:
$64^{2/3}$

Explanation:

Step1: Recall exponent rule

For \(a^{\frac{m}{n}}\), it can be rewritten as \((\sqrt[n]{a})^m\) or \(\sqrt[n]{a^m}\). Here, \(a = 64\), \(m = 2\), \(n = 3\). Let's use \((\sqrt[3]{64})^2\) first.

Step2: Find cube root of 64

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

Step3: Square the result

Now, square \(4\): \(4^2 = 16\).

Answer:

\(16\)