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

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Answer 1 · 2016-06-27T22:27:03

See explanation.

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

#(x^(1/3) + x^-(1/3))^2#

Is the same as writing:

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

Which can multiply out to be:

#x^(2/3) + x^(0) + x^(0) + x^(-2/3)#

Here we can combine like terms:

#x^(2/3) + 2(x^(0))+x^(-2/3)#

Which is ultimately:

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

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