Question

simplify. assume all variables are positive.
\\(\frac{x^{\frac{5}{2}}}{x^{\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: Use the quotient rule for exponents

When dividing two exponential expressions with the same base, we subtract the exponents. The rule is $\frac{x^m}{x^n}=x^{m - n}$ where $x$ is the base and $m,n$ are exponents. Here, the base is $x$, $m=\frac{5}{2}$ and $n = \frac{1}{2}$.
So, $\frac{x^{\frac{5}{2}}}{x^{\frac{1}{2}}}=x^{\frac{5}{2}-\frac{1}{2}}$

Step2: Subtract the exponents

Calculate $\frac{5}{2}-\frac{1}{2}$. Since the denominators are the same, we subtract the numerators: $\frac{5 - 1}{2}=\frac{4}{2}=2$.
So, $x^{\frac{5}{2}-\frac{1}{2}}=x^{2}$

Answer:

$x^{2}$