How do you simplify (x^(1/3) + x^(-1/3))^2(x13+x13)2?

2 Answers
Nov 28, 2017

x^(2/3) + x^(-2/3) x23+x23

Explanation:

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

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(13)2+x(13)2

= x^(2/3) + x^(-2/3) =x23+x23

Nov 28, 2017

=x^(2/3)+x^(-2/3)+2=x23+x23+2

Explanation:

->(a+b)^2=a^2+2ab+b^2:(a+b)2=a2+2ab+b2:
->color(red)(x^a)^b=x^(ab)xab=xab
->color(red)(x^a)*x^-a=x^0=1xaxa=x0=1

(x^(1/3)+x^(-1/3))^2(x13+x13)2

=x^(2/3)+2x^(1/3)x^(-1/3)+x^(-2/3)=x23+2x13x13+x23

=x^(2/3)+x^(-2/3)+2=x23+x23+2