Question

1. ★ (u4 l6 p5) evaluate $8^{\frac{5}{3}}$. $8^{\frac{5}{3}} = \sqrt3{8^5}$

Explanation:

Step1: Recall exponent rule

For \(a^{\frac{m}{n}}\), it can be written as \(\sqrt[n]{a^m}\) or \((\sqrt[n]{a})^m\). Here, \(a = 8\), \(m = 5\), \(n = 3\). We can also use the property \((a^m)^n=a^{mn}\). Let's rewrite \(8^{\frac{5}{3}}\) as \((8^{\frac{1}{3}})^5\).

Step2: Calculate \(8^{\frac{1}{3}}\)

We know that \(2^3 = 8\), so \(\sqrt[3]{8}=2\), which means \(8^{\frac{1}{3}} = 2\).

Step3: Raise to the 5th power

Now, we have \((8^{\frac{1}{3}})^5=2^5\). And \(2^5=32\).

Answer:

\(32\)