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

User Bantic
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1 Answer

2 votes

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)}

User Virtualeyes
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