Simplify. Assume all variables are positive. $\newline$ $\frac{b^{\frac{3}{2}}}{b^{\frac{5}{2}}}$ $\newline$ 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. $\newline$ ______

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{b^{\frac{3}{2}}}{b^{\frac{5}{2}}}

\newline

Write your answer in the form

A

\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 Expression: Identify the expression to simplify. $\newline$ We have the expression $b^{\frac{3}{2}} / b^{\frac{5}{2}}$ . We need to simplify this expression using the properties of exponents.
Apply Quotient Rule: Apply the quotient rule for exponents. $\newline$ The quotient rule states that when dividing like bases with exponents, we subtract the exponents: $a^m / a^n = a^{(m-n)}$ . $\newline$ So, $b^{3/2} / b^{5/2} = b^{(3/2 - 5/2)}$ .
Perform Subtraction: Perform the subtraction of the exponents. $\newline$ Subtract the exponents: $\frac{3}{2} - \frac{5}{2} = -\frac{2}{2}$ .
Simplify Result: Simplify the result. $\newline$ Since $-\frac{2}{2}$ is equal to $-1$ , we have $b^{-1}$ .
Write Final Answer: Write the final answer with a positive exponent. $\newline$ To express $b^{-1}$ with a positive exponent, we take the reciprocal of $b$ , which is $\frac{1}{b}$ .