Question

simplify. assume all variables are positive.
$(8r^{3})^{\frac{4}{3}}$
write your answer in the form $a$ or $\frac{a}{b}$, where $a$ and $b$ are constants or variable expressions that have no variables in common. all exponents in your answer should be positive.

Explanation:

Step1: Apply exponent product rule

$$(8r^3)^{\frac{4}{3}} = 8^{\frac{4}{3}} \cdot (r^3)^{\frac{4}{3}}$$

Step2: Simplify constant term

$$8^{\frac{4}{3}} = (8^{\frac{1}{3}})^4 = 2^4 = 16$$

Step3: Simplify variable term

$$(r^3)^{\frac{4}{3}} = r^{3 \cdot \frac{4}{3}} = r^4$$

Step4: Combine simplified terms

$$16 \cdot r^4 = 16r^4$$

Answer:

$16r^4$