How do you simplify ${(x^{\frac{1}{3}} + x^{- \frac{1}{3}})}^{2}$ $(x^(1/3) + x^(-1/3))^2$ ?

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How do you simplify ${(x^{\frac{1}{3}} + x^{- \frac{1}{3}})}^{2}$ $(x^(1/3) + x^(-1/3))^2$ ?

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Answer 1 · 2017-11-28T01:09:34

$x^{\frac{2}{3}} + x^{- \frac{2}{3}}$ $x^(2/3) + x^(-2/3)$

Explanation:

Remember the exponent laws
${(x^{m})}^{n} = x^{m n}$ $(x^m)^n = x^(mn)$

Since they have the common x, you can separate the equation if that’s easier, so:

$x^{(\frac{1}{3}) \cdot 2} + x^{(- \frac{1}{3}) \cdot 2}$ $x^((1/3)*2) + x^((-1/3)*2)$

$= x^{\frac{2}{3}} + x^{- \frac{2}{3}}$ $= x^(2/3) + x^(-2/3)$

Answer 2 · 2017-11-28T13:20:54

$= x^{\frac{2}{3}} + x^{- \frac{2}{3}} + 2$ $=x^(2/3)+x^(-2/3)+2$

Explanation:

$\to {(a + b)}^{2} = a^{2} + 2 a b + b^{2} :$ $->(a+b)^2=a^2+2ab+b^2:$
$\to {x^{a}}^{b} = x^{a b}$ $->color(red)(x^a)^b=x^(ab)$
$\to x^{a} \cdot x^{- a} = x^{0} = 1$ $->color(red)(x^a)*x^-a=x^0=1$

${(x^{\frac{1}{3}} + x^{- \frac{1}{3}})}^{2}$ $(x^(1/3)+x^(-1/3))^2$

$= x^{\frac{2}{3}} + 2 x^{\frac{1}{3}} x^{- \frac{1}{3}} + x^{- \frac{2}{3}}$ $=x^(2/3)+2x^(1/3)x^(-1/3)+x^(-2/3)$

$= x^{\frac{2}{3}} + x^{- \frac{2}{3}} + 2$ $=x^(2/3)+x^(-2/3)+2$

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How do you simplify ${(x^{\frac{1}{3}} + x^{- \frac{1}{3}})}^{2}$ $(x^(1/3) + x^(-1/3))^2$ ?

2 Answers

Explanation:

Explanation:

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