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

Question

1584 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-11-28T01:09:34

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

Remember the exponent laws
#(x^m)^n = x^(mn)#

Since they have the common x, you can separate the equation if that’s easier, so:

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

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

Answer 2 · 2017-11-28T13:20:54

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

#->(a+b)^2=a^2+2ab+b^2:#
#->color(red)(x^a)^b=x^(ab)#
#->color(red)(x^a)*x^-a=x^0=1#

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

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

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