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Simplify. Assume all variables are positive. $\newline$ $\frac{d^{\frac{4}{3}}}{d^{\frac{7}{3}}}$ $\newline$ 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{d^{\frac{4}{3}}}{d^{\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 Expression: We have the expression: $\newline$ $d^{\frac{4}{3}}/d^{\frac{7}{3}}$ $\newline$ To simplify this expression, we need to subtract the exponents because when dividing powers with the same base, we subtract the exponents.
Subtract Exponents: Subtract the exponents: $d^{\frac{4}{3}}/d^{\frac{7}{3}} = d^{(\frac{4}{3})-(\frac{7}{3})}$ Perform the subtraction: $d^{(\frac{4}{3})-(\frac{7}{3})} = d^{-\frac{3}{3}}$
Perform Subtraction: Simplify the exponent: $\newline$ $d^{(-3/3)} = d^{(-1)}$ $\newline$ Since we want the exponent to be positive, we rewrite the expression using the property that $a^{(-n)} = \frac{1}{a^n}$ : $\newline$ $d^{(-1)} = \frac{1}{d}$

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