Simplify:
x^1/3[x^1/2 +2x^2]

answers:
A) x^1/6 + 2x^2/3
B) x^2/5 + 2x^7/3
C) x^2/5 + 2x^3/4
D) x^5/6+ 2x^7/3

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Taeyongismyhusband Taeyongismyhusband · Answer 1 · 2018-04-15T03:32:48+02:00

A) x^1/6 + 2x^2/33

If you multiply each one of the exponents in the parentheses by the exponent outside the parentheses you get the answer.

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MrRoyal MrRoyal · Answer 2 · 2021-12-10T10:54:20+01:00

The simplified expression of [tex]x^{1/3}(x^{1/2} + 2x^2)[/tex] is (d) [tex]x^{\frac56} + 2x^{\frac{7}{2}}[/tex]

The expression is given as:

[tex]x^{1/3}(x^{1/2} + 2x^2)[/tex]

Start by opening the bracket

[tex]x^{1/3}(x^{1/2} + 2x^2) = x^{1/3} \times x^{1/2} + x^{1/3} \times 2x^2[/tex]

Apply law of indices

[tex]x^{1/3}(x^{1/2} + 2x^2) = x^{1/3+1/2} + x^{1/3} \times 2x^2[/tex]

Take LCM

[tex]x^{1/3}(x^{1/2} + 2x^2) = x^{\frac{2 + 3}{6}} + x^{1/3} \times 2x^2[/tex]

[tex]x^{1/3}(x^{1/2} + 2x^2) = x^{\frac56} + x^{1/3} \times 2x^2[/tex]

Rewrite the expression as:

[tex]x^{1/3}(x^{1/2} + 2x^2) = x^{\frac56} + 2x^{1/3} \times x^2[/tex]

Apply law of indices again

[tex]x^{1/3}(x^{1/2} + 2x^2) = x^{\frac56} + 2x^{1/3 + 2}[/tex]

Take LCM

[tex]x^{1/3}(x^{1/2} + 2x^2) = x^{\frac56} + 2x^{\frac{1 + 6}{2}}[/tex]

[tex]x^{1/3}(x^{1/2} + 2x^2) = x^{\frac56} + 2x^{\frac{7}{2}}[/tex]

Hence, the simplified expression of [tex]x^{1/3}(x^{1/2} + 2x^2)[/tex] is (d) [tex]x^{\frac56} + 2x^{\frac{7}{2}}[/tex]

Read more about simplifying expressions at:

https://brainly.com/question/8690932