Question

simplify. assume all variables are positive. \\(\frac{v^{\frac{3}{5}}}{v^{\frac{14}{5}}}\\) 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: \( \frac{v^a}{v^b} = v^{a - b} \). Here, the base is \( v \), \( a=\frac{3}{5} \), and \( b = \frac{14}{5} \). So we have \( v^{\frac{3}{5}-\frac{14}{5}} \).

Step2: Subtract the exponents

Calculate \( \frac{3}{5}-\frac{14}{5}=\frac{3 - 14}{5}=\frac{- 11}{5} \). So now we have \( v^{-\frac{11}{5}} \).

Step3: Use negative exponent rule

The negative exponent rule states that \( v^{-n}=\frac{1}{v^n} \), so \( v^{-\frac{11}{5}}=\frac{1}{v^{\frac{11}{5}}} \).

Answer:

\( \frac{1}{v^{\frac{11}{5}}} \)