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Simplify. Assume all variables are positive. $\newline$ $\frac{z^{\frac{7}{4}}}{z^{\frac{9}{4}}}$ $\newline$ 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{7}{4}}}{z^{\frac{9}{4}}}

\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 Rule for Dividing Powers: We have the expression: $\newline$ $z^{\frac{7}{4}}/z^{\frac{9}{4}}$ $\newline$ To simplify this expression, we need to apply the rule for dividing powers with the same base, which states that we should subtract the exponents.
Subtract Exponents: Subtract the exponents of $z$ : $z^{7/4} / z^{9/4} = z^{(7/4) - (9/4)}$ Perform the subtraction: $z^{(7/4) - (9/4)} = z^{-2/4}$
Simplify Exponent: Simplify the exponent: $z^{(-2/4)} = z^{(-1/2)}$ Since we want the exponent to be positive, we rewrite the expression with a positive exponent: $z^{(-1/2)} = \frac{1}{z^{(1/2)}}$

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