Question

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

Answer 1

Start by writing the expansion:

`(x^(1/3) + x^(-1/3))(x^(1/3) + x^(-1/3))`

Now, combine using the exponent rule `a^n xx a^m = a^(n + m)`:

`=x^(1/3 + 1/3) + x^(-1/3 + 1/3) + x^(-1/3 + -1/3) + x^(-1/3 + 1/3)`

`=x^(2/3) + x^0 + x^(-2/3) + x^0`

`=x^(2/3) + x^(-2/3) + 2`

If you want the answer without negative exponents, simply use the rule `a^(-n) = 1/a^n`:

`=2 + x^(2/3) + 1/x^(2/3)`

Hopefully the helps!