Question

simplify.
\\(\frac{v^{\frac{3}{4}}}{v^{\frac{5}{8}}}\\)
write your answer using only a positive exponent.
assume that the variable represents a positive real number.

Explanation:

Step1: Apply exponent quotient rule

When dividing like bases, subtract exponents: $\frac{v^a}{v^b}=v^{a-b}$
$\frac{v^{\frac{3}{4}}}{v^{\frac{5}{8}}}=v^{\frac{3}{4}-\frac{5}{8}}$

Step2: Subtract the fractions

Find a common denominator (8) for the exponents:
$\frac{3}{4}-\frac{5}{8}=\frac{6}{8}-\frac{5}{8}=\frac{1}{8}$
So $v^{\frac{6}{8}-\frac{5}{8}}=v^{\frac{1}{8}}$

Answer:

$v^{\frac{1}{8}}$