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

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Answer 1 · 2016-08-17T01:02:29

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!