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Simplify. Assume all variables are positive. $\newline$ $\frac{z^{\frac{9}{4}}}{z^{\frac{5}{4}}}$ $\newline$ 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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Division with rational exponents

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{z^{\frac{9}{4}}}{z^{\frac{5}{4}}}

\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

______

Identify Operation: Identify the operation to be applied with the exponents. $\newline$ When dividing powers with the same base, subtract the exponents.
Subtract Exponents: Subtract the exponents of $z$ . $\newline$ $\frac{z^{\frac{9}{4}}}{z^{\frac{5}{4}}} = z^{\left(\frac{9}{4} - \frac{5}{4}\right)}$ $\newline$ = $z^{\frac{4}{4}}$ $\newline$ = $z^1$
Simplify Expression: Simplify the expression. Since $z^1$ is simply $z$ , the expression simplifies to: $z$

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