Question

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

Answer 1

`x^{(1)/(3)}\:* \left(x^{(1)/(2)}\:+\:2x^2\right)=x^{(5)/(6)}+2x^{(7)/(3)}`

Explanation:

`x^{(1)/(3)}\:* \left(x^{(1)/(2)}\:+\:2x^2\right)`

Let us simplify the expression

`x^{(1)/(3)}\:* \left(x^{(1)/(2)}\:+\:2x^2\right)`

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

`a=x^{(1)/(3)},\:b=x^{(1)/(2)},\:c=2x^2`

so

`=x^{(1)/(3)}x^{(1)/(2)}+x^{(1)/(3)}* \:2x^2`

`=x^{(1)/(3)}x^{(1)/(2)}+2x^2x^{(1)/(3)}`

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

so the expression becomes

`=x^{(5)/(6)}+2x^{(7)/(3)}`

Thus,

`x^{(1)/(3)}\:* \left(x^{(1)/(2)}\:+\:2x^2\right)=x^{(5)/(6)}+2x^{(7)/(3)}`