Question

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

Explanation:

Step1: Evaluate \( 64^{\frac{1}{3}} \)

Recall the exponent rule \( a^{\frac{1}{n}}=\sqrt[n]{a} \). For \( 64^{\frac{1}{3}} \), we need to find the cube root of 64. We know that \( 4^3 = 64 \), so \( \sqrt[3]{64}=4 \). Thus, \( 64^{\frac{1}{3}} = 4 \).

Step2: Evaluate \( 625^{\frac{1}{4}} \)

Using the same exponent rule \( a^{\frac{1}{n}}=\sqrt[n]{a} \), for \( 625^{\frac{1}{4}} \), we find the fourth root of 625. We know that \( 5^4 = 625 \) (since \( 5\times5\times5\times5 = 25\times25 = 625 \)), so \( \sqrt[4]{625}=5 \). Thus, \( 625^{\frac{1}{4}} = 5 \).

Answer:

\( 64^{\frac{1}{3}} = \boldsymbol{4} \)
\( 625^{\frac{1}{4}} = \boldsymbol{5} \)