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Simplify. Assume all variables are positive. $\newline$ $\frac{d^{\frac{4}{3}}}{d^{\frac{2}{3}}}$ $\newline$ 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{d^{\frac{4}{3}}}{d^{\frac{2}{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 Operation: Apply the operation to the exponents. $\newline$ $(d^{\frac{4}{3}}) / (d^{\frac{2}{3}}) = d^{(\frac{4}{3} - \frac{2}{3})}$
Perform Subtraction: Perform the subtraction of the exponents. $d^{(\frac{4}{3}) - (\frac{2}{3})} = d^{\frac{2}{3}}$
Write Final Answer: Write the final answer with a positive exponent. $\newline$ The final answer is $d^{\frac{2}{3}}$ .

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