Question

simplify.
$\frac{v^{\frac{4}{5}}}{v^{\frac{2}{3}}}$
write your answer using only a positive exponent.
assume that the variable represents a positive real number.

Explanation:

Step1: Apply exponent division rule

When dividing terms with the same base, subtract the denominator exponent from the numerator exponent: $v^{\frac{4}{5} - \frac{2}{3}}$

Step2: Find common denominator for fractions

The common denominator of 5 and 3 is 15. Convert the fractions: $\frac{4}{5} = \frac{12}{15}$, $\frac{2}{3} = \frac{10}{15}$

Step3: Subtract the fractions

$\frac{12}{15} - \frac{10}{15} = \frac{2}{15}$

Answer:

$v^{\frac{2}{15}}$