Question

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

Answer 1

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

Explanation:

making use of the laws of exponents :

`• a^m xx a^n = a^(m+n)`

`• a^0 = 1`

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

distribute the brackets using FOIL (or any method you have)

`= x^(1/3)xxx^(1/3) + x^(-1/3)xxx^(1/3)+ x^(-1/3)xxx^(1/3)+x^(-1/3)xxx^(-1/3)`
( using the above laws to simplify )

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

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