Question

simplify. assume all variables are positive.
$\frac{v^{\frac{9}{4}}}{v^{\frac{11}{4}}}$
write your answer in the form a or $\frac{a}{b}$, where a and b are constants that have no variables in common. all exponents in your answer sh

Explanation:

Step1: Apply exponent division rule

When dividing terms with the same base, subtract exponents: $v^{\frac{a}{b}} \div v^{\frac{c}{b}} = v^{\frac{a}{b}-\frac{c}{b}}$
$\frac{v^{\frac{9}{4}}}{v^{\frac{11}{4}}} = v^{\frac{9}{4}-\frac{11}{4}}$

Step2: Calculate the exponent

Subtract the numerators over the common denominator.
$v^{\frac{9-11}{4}} = v^{\frac{-2}{4}}$

Step3: Simplify the exponent

Reduce the fraction to lowest terms.
$v^{-\frac{1}{2}} = \frac{1}{v^{\frac{1}{2}}}$

Answer:

$\frac{1}{v^{\frac{1}{2}}}$