Question

simplify. assume all variables are positive.\\(\frac{v^{\frac{4}{3}}}{v^{\frac{7}{3}}}\\)\
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: Apply exponent subtraction rule

When dividing like bases, subtract exponents: $v^{\frac{4}{3} - \frac{7}{3}}$

Step2: Calculate the exponent

$\frac{4}{3} - \frac{7}{3} = \frac{4-7}{3} = -\frac{3}{3} = -1$

Step3: Rewrite with positive exponent

A negative exponent means reciprocal: $v^{-1} = \frac{1}{v}$

Answer:

$\frac{1}{v}$