Question

(e) $\frac{3a^{3/2} cdot a^{1/2}}{a^{-1}}$

Explanation:

Step1: Multiply terms in numerator

When multiplying like bases, add exponents: $a^m \cdot a^n = a^{m+n}$
$3a^{\frac{3}{2}} \cdot a^{\frac{1}{2}} = 3a^{\frac{3}{2}+\frac{1}{2}} = 3a^{2}$

Step2: Divide by denominator term

When dividing like bases, subtract exponents: $\frac{a^m}{a^n} = a^{m-n}$
$\frac{3a^{2}}{a^{-1}} = 3a^{2 - (-1)} = 3a^{3}$

Answer:

$3a^3$