Question

simplify. assume all variables are positive.
$b^{\frac{5}{2}} \cdot b^{\frac{5}{2}}$
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: $b^m \cdot b^n = b^{m+n}$
$b^{\frac{5}{2}} \cdot b^{\frac{5}{2}} = b^{\frac{5}{2}+\frac{5}{2}}$

Step2: Add the exponents

Calculate the sum of the fractions
$b^{\frac{5+5}{2}} = b^{\frac{10}{2}}$

Step3: Simplify the exponent

Reduce the fraction to a whole number
$b^{5}$

Answer:

$b^5$