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Simplify. Assume all variables are positive. $\newline$ $\frac{z^{\frac{13}{6}}}{z^{\frac{5}{6}}}$ $\newline$ Write your answer in the form $A$ or $A/B$ , where $A$ and $B$ are constants or variable expressions that have no variables in common. All exponents in your answer should be positive. $\newline$ ______

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Simplify expressions involving rational exponents II

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{z^{\frac{13}{6}}}{z^{\frac{5}{6}}}

\newline

Write your answer in the form

A

or

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.

\newline

______

Combine Exponents: Write $z^{\frac{13}{6}} / z^{\frac{5}{6}}$ as a single power of $z$ by subtracting the exponents. $\newline$ When dividing powers with the same base, we subtract the exponents. $\newline$ $z^{\frac{13}{6}} / z^{\frac{5}{6}}$ $\newline$ = $z^{(\frac{13}{6} - \frac{5}{6})}$ $\newline$ = $z^{\frac{8}{6}}$
Simplify Fraction: Simplify the exponent $\frac{8}{6}$ . $\frac{8}{6}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\frac{8}{6} = \frac{4}{3}$ So, $z^{\frac{8}{6}}$ becomes $z^{\frac{4}{3}}$ .
Final Answer Format: Write the final answer in the form $A$ or $A/B$ with positive exponents. $\newline$ The simplified form of $z^{13/6} / z^{5/6}$ is $z^{4/3}$ .

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