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Simplify. Assume all variables are positive. $\newline$ $\frac{z^{\frac{2}{3}}}{z^{\frac{4}{3}}}$ $\newline$ 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{2}{3}}}{z^{\frac{4}{3}}}

\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.
Apply Exponent Rule: Apply the exponent subtraction rule to simplify the expression. $\newline$ $\frac{z^{\frac{2}{3}}}{z^{\frac{4}{3}}} = z^{\left(\frac{2}{3}-\frac{4}{3}\right)} = z^{-\frac{2}{3}}$
Rewrite with Positive Exponent: Since we want the exponent to be positive, rewrite the expression with a positive exponent. $\newline$ $z^{(-\frac{2}{3})} = \frac{1}{z^{(\frac{2}{3})}}$

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