# How do you simplify  (x^(1/3) + x^(-1/3))^2?

Nov 28, 2017

${x}^{\frac{2}{3}} + {x}^{- \frac{2}{3}}$

#### Explanation:

Remember the exponent laws
${\left({x}^{m}\right)}^{n} = {x}^{m n}$

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

${x}^{\left(\frac{1}{3}\right) \cdot 2} + {x}^{\left(- \frac{1}{3}\right) \cdot 2}$

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

Nov 28, 2017

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

#### Explanation:

$\to {\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2} :$
$\to {\textcolor{red}{{x}^{a}}}^{b} = {x}^{a b}$
$\to \textcolor{red}{{x}^{a}} \cdot {x}^{-} a = {x}^{0} = 1$

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

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

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