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

Explanation:

Step1: Apply distributive property

$x^{\frac{1}{3}}(x^{\frac{1}{2}} + 2x^{2})=x^{\frac{1}{3}}\times x^{\frac{1}{2}}+x^{\frac{1}{3}}\times2x^{2}$

Step2: Use exponent - rule $a^{m}\times a^{n}=a^{m + n}$

$x^{\frac{1}{3}}\times x^{\frac{1}{2}}=x^{\frac{1}{3}+\frac{1}{2}}=x^{\frac{2 + 3}{6}}=x^{\frac{5}{6}}$ and $x^{\frac{1}{3}}\times2x^{2}=2x^{\frac{1}{3}+2}=2x^{\frac{1 + 6}{3}}=2x^{\frac{7}{3}}$

Answer:

$x^{\frac{5}{6}}+2x^{\frac{7}{3}}$