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Simplify. Assume all variables are positive. $\newline$ $\frac{z^{\frac{1}{4}}}{z^{\frac{7}{4}}}$ $\newline$ 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 II

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{z^{\frac{1}{4}}}{z^{\frac{7}{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

______

Combine powers of $z$ : Write $z^{1/4}/z^{7/4}$ as a single power of $z$ . $\newline$ When dividing powers with the same base, we subtract the exponents. $\newline$ $z^{1/4}/z^{7/4}$ $\newline$ = $z^{(1/4)-(7/4)}$ $\newline$ = $z^{-6/4}$
Simplify the exponent: Simplify the exponent. $z^{(-6/4)}$ can be simplified by reducing the fraction $-6/4$ . $z^{(-6/4)} = z^{(-3/2)}$
Express with positive exponent: Express $z^{-3/2}$ with a positive exponent. $\newline$ According to the negative exponent rule: $\newline$ $a^{-m} = \frac{1}{a^m}$ $\newline$ $z^{-3/2} = \frac{1}{z^{3/2}}$

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