Question

simplify. assume all variables are positive.
\\(\frac{v^{\frac{3}{2}}}{v^{\frac{5}{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 exponent rule for division

When dividing exponents with the same base, we subtract the exponents: $a^m \div a^n = a^{m - n}$. So for $\frac{v^{\frac{3}{2}}}{v^{\frac{5}{2}}}$, we have $v^{\frac{3}{2}-\frac{5}{2}}$.

Step2: Subtract the exponents

Calculate $\frac{3}{2}-\frac{5}{2}=\frac{3 - 5}{2}=\frac{-2}{2}=-1$. So the expression becomes $v^{-1}$.

Step3: Rewrite negative exponent

A negative exponent means the reciprocal: $a^{-n}=\frac{1}{a^n}$. So $v^{-1}=\frac{1}{v}$.

Answer:

$\frac{1}{v}$