Question

evaluate.
\\( 625^{\frac{1}{4}} = \square \\)
\\( 64^{\frac{1}{3}} = \square \\)

Explanation:

Step1: Evaluate \( 625^{\frac{1}{4}} \)

Recall that \( a^{\frac{1}{n}}=\sqrt[n]{a} \). So, \( 625^{\frac{1}{4}}=\sqrt[4]{625} \). Since \( 5^4 = 5\times5\times5\times5 = 625 \), then \( \sqrt[4]{625}=5 \).

Step2: Evaluate \( 64^{\frac{1}{3}} \)

Using the same rule \( a^{\frac{1}{n}}=\sqrt[n]{a} \), we have \( 64^{\frac{1}{3}}=\sqrt[3]{64} \). And since \( 4^3 = 4\times4\times4 = 64 \), then \( \sqrt[3]{64}=4 \).

Answer:

For \( 625^{\frac{1}{4}} \), the answer is \( 5 \).
For \( 64^{\frac{1}{3}} \), the answer is \( 4 \).