Answer
$a^{\frac{13}{6}}$
Work Step by Step
Step 1: $a^{\frac{1}{3}}a^{\frac{4}{3}}a^{\frac{1}{2}}$
Step 2: $a^{\frac{1}{3}+\frac{4}{3}+\frac{1}{2}}$
Step 3: Solving the expression in the index by taking LCM, $a^{\frac{2+8+3}{6}}$
Step 4: Simplifying, the expression becomes $a^{\frac{13}{6}}$
