Question

using properties of exponents
evaluate:
$8^{\frac{8}{3}} = \square$

Explanation:

Step1: Recall exponent property

Use the property \(a^{\frac{m}{n}}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m\). For \(8^{\frac{8}{3}}\), we can rewrite it as \((8^{\frac{1}{3}})^8\) or \(\sqrt[3]{8^8}\). First, find \(8^{\frac{1}{3}}\): since \(2^3 = 8\), \(8^{\frac{1}{3}}=2\).

Step2: Calculate the power

Now, raise this result to the 8th power: \(2^8\). Calculate \(2^8 = 256\).

Answer:

256