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

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{z^{\frac{3}{4}}}{z^{\frac{1}{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 Exponent Rule: We have the expression: $\newline$ $z^{\frac{3}{4}}/z^{\frac{1}{4}}$ $\newline$ Which operation will be applied with the exponents? $\newline$ When dividing powers with the same base, the exponents are subtracted.
Perform Subtraction: Apply the exponent rule for division: $z^{\frac{3}{4}}/z^{\frac{1}{4}} = z^{\frac{3}{4} - \frac{1}{4}}$ Perform the subtraction of the exponents. $z^{\frac{3}{4} - \frac{1}{4}} = z^{\frac{2}{4}}$
Simplify Exponent: Simplify the exponent: $z^{\frac{2}{4}} = z^{\frac{1}{2}}$ This is because $\frac{2}{4}$ reduces to $\frac{1}{2}$ .

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