Question

simplify. assume all variables are positive.
$\frac{s^{\frac{1}{2}} cdot s^{\frac{5}{2}}}{s^{\frac{1}{2}}}$
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.

Explanation:

Step1: Add exponents in numerator

For like bases, $s^a \cdot s^b = s^{a+b}$. So:
$s^{\frac{1}{2}} \cdot s^{\frac{5}{2}} = s^{\frac{1}{2}+\frac{5}{2}} = s^{\frac{6}{2}} = s^3$

Step2: Subtract exponents (division)

For like bases, $\frac{s^a}{s^b} = s^{a-b}$. So:
$\frac{s^3}{s^{\frac{1}{2}}} = s^{3-\frac{1}{2}} = s^{\frac{6}{2}-\frac{1}{2}} = s^{\frac{5}{2}}$

Answer:

$s^{\frac{5}{2}}$