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Simplify. Assume all variables are positive. $\newline$ $\frac{z^{\frac{4}{3}}}{z^{\frac{7}{3}}}$ $\newline$ 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{4}{3}}}{z^{\frac{7}{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. $\newline$ $\frac{z^{\frac{4}{3}}}{z^{\frac{7}{3}}} = z^{\left(\frac{4}{3} - \frac{7}{3}\right)} = z^{-\frac{3}{3}}$
Simplify Expression: Simplify the exponent. $z^{(-3/3)} = z^{(-1)}$
Convert Negative Exponent: Convert the negative exponent to a positive exponent by taking the reciprocal. $z^{-1} = \frac{1}{z}$

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