Question

simplify. assume all variables are positive.
$c^{\frac{5}{2}} \div c^{\frac{3}{2}}$
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: Convert division to exponent subtraction

Recall that $x^a \div x^b = x^{a-b}$ for positive $x$.
$c^{\frac{5}{2}} \div c^{\frac{3}{2}} = c^{\frac{5}{2}-\frac{3}{2}}$

Step2: Simplify the exponent

Subtract the fractions in the exponent.
$c^{\frac{5-3}{2}} = c^{\frac{2}{2}} = c^1$

Step3: Simplify the final term

Any term to the power of 1 is itself.
$c^1 = c$

Answer:

$c$