Question

simplify: $x^{\frac{1}{3}}\left(x^{\frac{1}{2}} + 2x^{2}\
ight)$

Explanation:

Step1: Distribute the term

$x^{\frac{1}{3}} \cdot x^{\frac{1}{2}} + x^{\frac{1}{3}} \cdot 2x^2$

Step2: Add exponents for like bases

For $x^{\frac{1}{3}} \cdot x^{\frac{1}{2}}$: $\frac{1}{3}+\frac{1}{2}=\frac{2+3}{6}=\frac{5}{6}$, so $x^{\frac{5}{6}}$
For $x^{\frac{1}{3}} \cdot 2x^2$: $\frac{1}{3}+2=\frac{1+6}{3}=\frac{7}{3}$, so $2x^{\frac{7}{3}}$

Answer:

$x^{\frac{5}{6}} + 2x^{\frac{7}{3}}$ (matches the second option)