Question

simplify. assume all variables are positive.$z^{\frac{8}{3}} cdot z^{\frac{8}{3}}$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

When multiplying like bases, add exponents: $z^{\frac{4}{3}} \cdot z^{\frac{8}{3}} = z^{\frac{4}{3}+\frac{8}{3}}$

Step2: Calculate sum of exponents

$\frac{4}{3}+\frac{8}{3}=\frac{12}{3}=4$, so $z^{\frac{12}{3}}=z^4$

Answer:

$z^4$