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

Jun 27, 2016

See explanation.

#### Explanation:

A way we could simplify this is by multiplying out the expression.

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

Is the same as writing:

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

Which can multiply out to be:

${x}^{\frac{2}{3}} + {x}^{0} + {x}^{0} + {x}^{- \frac{2}{3}}$

Here we can combine like terms:

${x}^{\frac{2}{3}} + 2 \left({x}^{0}\right) + {x}^{- \frac{2}{3}}$

Which is ultimately:

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

Please note that there are many ways of getting to this simplified form.