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 - division rule

When dividing two powers with the same base \(a^m\div a^n=a^{m - n}\), here \(a = v\), \(m=\frac{3}{2}\), and \(n=\frac{5}{2}\). So \(\frac{v^{\frac{3}{2}}}{v^{\frac{5}{2}}}=v^{\frac{3}{2}-\frac{5}{2}}\).

Step2: Calculate the exponent

\(\frac{3}{2}-\frac{5}{2}=\frac{3 - 5}{2}=\frac{-2}{2}=-1\). So \(v^{\frac{3}{2}-\frac{5}{2}}=v^{-1}\).

Step3: Make the exponent positive

Using the rule \(a^{-n}=\frac{1}{a^{n}}\), for \(a = v\) and \(n = 1\), we get \(v^{-1}=\frac{1}{v}\).

Answer:

\(\frac{1}{v}\)