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Simplify. Assume all variables are positive. $\newline$ $\frac{x^{\frac{1}{4}}}{x^{\frac{11}{4}}}$ $\newline$ $\newline$ 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. $\newline$ ______ $\newline$

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Simplify expressions involving rational exponents I

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{x^{\frac{1}{4}}}{x^{\frac{11}{4}}}

\newline

\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

______

\newline

Subtracting exponents: Now we subtract the exponents: $\frac{1}{4} - \frac{11}{4} = -\frac{10}{4}$ . This simplifies to $-\frac{5}{2}$ because $-10$ divided by $4$ is $-5$ .
Applying negative exponent rule: We then apply the rule for negative exponents, which is $a^{-m} = \frac{1}{a^m}$ . $\newline$ So, $x^{-\frac{5}{2}}$ becomes $\frac{1}{x^{\frac{5}{2}}}$ .

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