Question

Simplify : x ^ (1/3) * (x ^ (1/2) + 2x ^ 2)

Answer 1

Answer:

$x^{\frac{1}{3}}\:\times \left(x^{\frac{1}{2}}\:+\:2x^2\right)=x^{\frac{5}{6}}+2x^{\frac{7}{3}}$

Step-by-step explanation:

$x^{\frac{1}{3}}\:\times \left(x^{\frac{1}{2}}\:+\:2x^2\right)$

Let us simplify the expression

$x^{\frac{1}{3}}\:\times \left(x^{\frac{1}{2}}\:+\:2x^2\right)$

$\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac$

$a=x^{\frac{1}{3}},\:b=x^{\frac{1}{2}},\:c=2x^2$

so

$=x^{\frac{1}{3}}x^{\frac{1}{2}}+x^{\frac{1}{3}}\times \:2x^2$

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

$\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}$

so the expression becomes

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

Thus,

$x^{\frac{1}{3}}\:\times \left(x^{\frac{1}{2}}\:+\:2x^2\right)=x^{\frac{5}{6}}+2x^{\frac{7}{3}}$