Question

simplify. assume all variables are positive.
$v^{\frac{7}{4}} \cdot v^{\frac{7}{4}}$
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 like bases, add exponents: $x^a \cdot x^b = x^{a+b}$
$v^{\frac{7}{4}} \cdot v^{\frac{7}{4}} = v^{\frac{7}{4}+\frac{7}{4}}$

Step2: Add the fractions

Sum the numerators over the common denominator
$v^{\frac{7+7}{4}} = v^{\frac{14}{4}}$

Step3: Simplify the exponent

Reduce the fraction to lowest terms
$v^{\frac{7}{2}}$

Answer:

$v^{\frac{7}{2}}$