Question

evaluate.
\\(256^{\frac{1}{4}} = \square\\)
\\(343^{\frac{1}{3}} = \square\\)

Explanation:

Step1: Evaluate \( 256^{\frac{1}{4}} \)

Recall that \( a^{\frac{1}{n}}=\sqrt[n]{a} \). So, \( 256^{\frac{1}{4}}=\sqrt[4]{256} \). We know that \( 4^4 = 256 \), so \( \sqrt[4]{256}=4 \).

Step2: Evaluate \( 343^{\frac{1}{3}} \)

Using the same rule \( a^{\frac{1}{n}}=\sqrt[n]{a} \), \( 343^{\frac{1}{3}}=\sqrt[3]{343} \). Since \( 7^3 = 343 \), we have \( \sqrt[3]{343}=7 \).

Answer:

\( 256^{\frac{1}{4}} = \boldsymbol{4} \)
\( 343^{\frac{1}{3}} = \boldsymbol{7} \)