Question

Simplify:

`( x^a/x^b)^( a^2 + ab + b^2 ) xx (x^b/x^c)^(b^2 + bc + c^2) xx (x^c/x^a)^( c^2 + ca + a^2 )`

Answer 1

`(x^a/x^b)^(a^2 + ab + b^2) xx (x^b/x^c)^(b^2 + bc + c^2) xx (x^c/x^a)^(c^2 + ca + a^2)`

= `( x^(a - b))^(a^2 + ab + b^2) xx (x^(b - c))^(b^2 + bc + c^2) xx ( x^(c - a ))^(c^2 + ca + a^2)`

= `x^(a^3 - b^3) xx x^(b^3 - c^3 ) xx x^(c^3 - a^3)`

= `x^(a^3 - b^3 + b^3 - c^3 + c^3 -a^3)`

= `x^0`

= 1