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Simplify. Assume all variables are positive. $\newline$ $\frac{b^{\frac{9}{4}}}{b^{\frac{5}{4}}}$ $\newline$ 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{b^{\frac{9}{4}}}{b^{\frac{5}{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

______

Identify base and operation: We have the expression: $b^{\frac{9}{4}} / b^{\frac{5}{4}}$ Which operation will be applied with exponent? When dividing powers with the same base, the exponents are subtracted.
Apply rule for dividing powers: Simplify the expression by subtracting the exponents. $\newline$ $b^{\frac{9}{4}} / b^{\frac{5}{4}}$ $\newline$ = $b^{\frac{9}{4} - \frac{5}{4}}$ $\newline$ = $b^{\frac{4}{4}}$ $\newline$ = $b^1$ $\newline$ Since any number to the power of $1$ is itself, we can simplify this further to just $b$ .

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