Question

simplify. assume all variables are positive.$v^{\frac{11}{4}} cdot v^{\frac{11}{4}}$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 product rule

When multiplying terms with the same base, add exponents: $v^a \cdot v^b = v^{a+b}$
$\displaystyle v^{\frac{11}{4}} \cdot v^{\frac{11}{4}} = v^{\frac{11}{4}+\frac{11}{4}}$

Step2: Add the fractions

Sum the numerators over the common denominator
$\displaystyle v^{\frac{11+11}{4}} = v^{\frac{22}{4}}$

Step3: Simplify the exponent

Reduce the fraction to lowest terms
$\displaystyle v^{\frac{11}{2}}$

Answer:

$\displaystyle v^{\frac{11}{2}}$