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Simplify. Assume all variables are positive. $\newline$ $\frac{z^{\frac{9}{5}}}{z^{\frac{6}{5}}}$ $\newline$ 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

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{z^{\frac{9}{5}}}{z^{\frac{6}{5}}}

\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 Equation & Apply Quotient Rule: Identify the equation and apply the quotient rule for exponents. $\newline$ The quotient rule states that when dividing like bases with exponents, you subtract the exponents: $a^m / a^n = a^{m-n}$ . $\newline$ $z^{9/5} / z^{6/5} = z^{9/5 - 6/5}$
Subtract Exponents: Subtract the exponents. $\newline$ Subtract the exponents by finding the difference between $\frac{9}{5}$ and $\frac{6}{5}$ . $\newline$ $\frac{9}{5} - \frac{6}{5} = \frac{3}{5}$ $\newline$ So, $z^{\frac{9}{5}} / z^{\frac{6}{5}} = z^{\frac{3}{5}}$
Write Final Answer: Write the final answer. $\newline$ Since all exponents are positive and there are no variables in common in the numerator and denominator, the expression is already in the correct form. $\newline$ The final answer is $z^{\frac{3}{5}}$ .

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