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Simplify. Assume all variables are positive. $\newline$ $\frac{d^{\frac{1}{3}}}{d^{\frac{4}{3}}}$ $\newline$ 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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Simplify expressions involving rational exponents

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{d^{\frac{1}{3}}}{d^{\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

______

Apply Exponent Rule: We have the expression: $\newline$ $d^{\frac{1}{3}}/d^{\frac{4}{3}}$ $\newline$ Which operation will be applied with the exponents? $\newline$ When dividing powers with the same base, the exponents are subtracted.
Simplify Expression: We apply the exponent rule: $\newline$ $d^{\frac{1}{3}}/d^{\frac{4}{3}}$ $\newline$ Simplify the expression by subtracting the exponents. $\newline$ $d^{\frac{1}{3} - \frac{4}{3}}$ $\newline$ = $d^{-\frac{3}{3}}$ $\newline$ = $d^{-1}$
Convert Negative Exponent: We need to express the answer with a positive exponent. $\newline$ To convert a negative exponent to a positive exponent, we take the reciprocal of the base. $\newline$ $d^{-1} = \frac{1}{d}$

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