Simplify 3b^(1/2)*b^(3/2)

$3 b^{\frac{1}{2}} \cdot b^{\frac{3}{2}}$

Move $b^{\frac{3}{2}}$ .

$3 (b^{\frac{3}{2}} b^{\frac{1}{2}})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 b^{\frac{3}{2} + \frac{1}{2}}$

Combine the numerators over the common denominator.

$3 b^{\frac{3 + 1}{2}}$

Add $3$ and $1$ .

$3 b^{\frac{4}{2}}$

Divide $4$ by $2$ .

$3 b^{2}$