Question

simplify. assume all variables are positive.
$z^{\frac{11}{6}} \cdot z^{\frac{7}{6}}$
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 exponents with the same base, we add the exponents: \(a^m \cdot a^n = a^{m + n}\). Here, the base is \(z\), so \(z^{\frac{11}{6}} \cdot z^{\frac{7}{6}} = z^{\frac{11}{6}+\frac{7}{6}}\).

Step2: Add the exponents

Calculate \(\frac{11}{6}+\frac{7}{6}=\frac{11 + 7}{6}=\frac{18}{6}=3\). So the expression simplifies to \(z^3\).

Answer:

\(z^3\)