Question

evaluate.
$16^{\frac{1}{4}} = $
$125^{\frac{1}{3}} = $

Explanation:

Step1: Evaluate \( 16^{\frac{1}{4}} \)

Recall that \( a^{\frac{1}{n}}=\sqrt[n]{a} \). For \( 16^{\frac{1}{4}} \), we need to find the 4th root of 16. Since \( 2^4 = 16 \), then \( \sqrt[4]{16}=2 \). So \( 16^{\frac{1}{4}} = 2 \).

Step2: Evaluate \( 125^{\frac{1}{3}} \)

Using the same property \( a^{\frac{1}{n}}=\sqrt[n]{a} \), for \( 125^{\frac{1}{3}} \), we find the 3rd root of 125. Since \( 5^3 = 125 \), then \( \sqrt[3]{125}=5 \). So \( 125^{\frac{1}{3}} = 5 \).

Answer:

For \( 16^{\frac{1}{4}} \), the answer is \( 2 \); for \( 125^{\frac{1}{3}} \), the answer is \( 5 \).