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Simplify. Assume all variables are positive. $\newline$ $\frac{z^{\frac{17}{6}}}{z^{\frac{7}{6}}}$ $\newline$ 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. $\newline$ ______

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Simplify expressions involving rational exponents II

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{z^{\frac{17}{6}}}{z^{\frac{7}{6}}}

\newline

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.

\newline

______

Subtract Exponents: Write $z^{\frac{17}{6}} / z^{\frac{7}{6}}$ as a single power of $z$ by subtracting the exponents. $\newline$ When dividing powers with the same base, we subtract the exponents. $\newline$ $z^{\frac{17}{6}} / z^{\frac{7}{6}} = z^{\left(\frac{17}{6} - \frac{7}{6}\right)}$
Perform Subtraction: Perform the subtraction of the exponents. $z^{(\frac{17}{6}) - (\frac{7}{6})} = z^{\frac{10}{6}}$
Simplify Exponent: Simplify the exponent by reducing the fraction. $z^{\frac{10}{6}}$ can be simplified because $10$ and $6$ have a common factor of $2$ . $z^{\frac{10}{6}} = z^{\frac{5}{3}}$
Final Answer: Write the final answer in the form $A$ or $A/B$ with positive exponents. $\newline$ The final simplified form of $z^{17/6} / z^{7/6}$ is $z^{5/3}$ .

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