question\nexpress $left(64^{\frac{1}{3}}\right)^2$ in simplest radical form.\nanswer attempt 1 out of 2

Explanation:

Step1: Apply exponent power rule

$(a^m)^n = a^{m \times n}$ $\left(64^{\frac{1}{3}}\right)^2 = 64^{\frac{1}{3} \times 2} = 64^{\frac{2}{3}}$

Step2: Rewrite exponent as radical

$a^{\frac{p}{q}} = \sqrt[q]{a^p}$ $64^{\frac{2}{3}} = \sqrt[3]{64^2}$

Step3: Simplify cube root of 64

$\sqrt[3]{64} = 4$, so $64 = 4^3$ $\sqrt[3]{(4^3)^2} = \sqrt[3]{4^6}$

Step4: Simplify the radical

$\sqrt[3]{4^6} = 4^{\frac{6}{3}} = 4^2$

Step5: Calculate final integer value

$4^2 = 16$ Alternatively, simplify directly: $\sqrt[3]{64^2} = \left(\sqrt[3]{64}\right)^2 = 4^2 = 16$

Answer:

$16$ or $\sqrt[3]{64^2}$ (simplest radical form reduces to the integer 16)