Question

evaluate without a calculator: $8^{2/3}$

Explanation:

Step1: Recall the formula for rational exponents

The formula for a rational exponent \(a^{\frac{m}{n}}\) is \(\sqrt[n]{a^m}\) or \((\sqrt[n]{a})^m\). For \(8^{\frac{2}{3}}\), we can use \((\sqrt[3]{8})^2\).

Step2: Calculate the cube root of 8

We know that \(\sqrt[3]{8} = 2\) because \(2\times2\times2 = 8\).

Step3: Square the result

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

Answer:

4