Question 1

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

Question 2

Answer:

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

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,

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

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