Simplify. Assume all variables are positive. $\newline$ $s^{\frac{5}{4}} \cdot s^{\frac{3}{4}}$ $\newline$ 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. $\newline$ ______

Full solution

Q. Simplify. Assume all variables are positive.

\newline

s^{\frac{5}{4}} \cdot s^{\frac{3}{4}}

\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 be simplified. $\newline$ We have the expression $s^{5/4} \times s^{3/4}$ and we need to simplify it.
Apply Exponent Property: Apply the property of exponents for multiplying with the same base. $\newline$ When multiplying expressions with the same base, we add the exponents: $a^m \times a^n = a^{m+n}$ . $\newline$ So, $s^{\frac{5}{4}} \times s^{\frac{3}{4}} = s^{\frac{5}{4} + \frac{3}{4}}$ .
Perform Exponent Addition: Perform the addition of the exponents. $\newline$ Add the fractions $\frac{5}{4}$ and $\frac{3}{4}$ . $\newline$ $\frac{5}{4} + \frac{3}{4} = \frac{(5 + 3)}{4} = \frac{8}{4}.$
Simplify Fraction: Simplify the fraction $\frac{8}{4}$ . The fraction $\frac{8}{4}$ simplifies to $2$ . So, $s^{\frac{8}{4}} = s^2$ .
Write Final Expression: Write the final simplified expression. $\newline$ The expression $s^{5/4} \times s^{3/4}$ simplifies to $s^2$ .