Question

simplify. assume all variables are positive.
$y^{\frac{5}{2}} \cdot y^{\frac{1}{2}}$
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 terms with the same base, add exponents: $y^{a} \cdot y^{b} = y^{a+b}$
So, $y^{\frac{5}{2}} \cdot y^{\frac{1}{2}} = y^{\frac{5}{2}+\frac{1}{2}}$

Step2: Add the fractions in exponent

$\frac{5}{2}+\frac{1}{2}=\frac{5+1}{2}=\frac{6}{2}=3$
Thus, $y^{\frac{6}{2}}=y^3$

Answer:

$y^3$