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

Aug 17, 2016

Start by writing the expansion:

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

Now, combine using the exponent rule ${a}^{n} \times {a}^{m} = {a}^{n + m}$:

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

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

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

If you want the answer without negative exponents, simply use the rule ${a}^{- n} = \frac{1}{a} ^ n$:

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

Hopefully the helps!