Question

1. ((64a^3)^{\frac{2}{3}})

Explanation:

Step1: Apply exponent product rule

$(64a^3)^{\frac{2}{3}} = 64^{\frac{2}{3}} \cdot (a^3)^{\frac{2}{3}}$

Step2: Simplify constant term

$64^{\frac{2}{3}} = (64^{\frac{1}{3}})^2 = 4^2 = 16$

Step3: Simplify variable term

$(a^3)^{\frac{2}{3}} = a^{3 \times \frac{2}{3}} = a^2$

Step4: Multiply simplified terms

$16 \cdot a^2$

Answer:

$16a^2$