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Question

`(x^a/x^b)^(a + b)`   .  `  (x^b/x^c)^(b + c)`   .`(x^c/x^a)^(c + a)`      = ?


Options:
A .  0
B .  `x^(abc)`
C .  `x^(a + b +c)`
D .  1
Answer: Option D

Given Exp. `x^((a - b) (a + b))`  .`x^((b - c) (b + c))` .`x^((c - a) (c + a))`

= `x^((a^2 - b^2))`. `x^((b^2 - c^2))`.`x^((c^2 - a^2))`

=`x^((a^2 - b^2  + b^2 -c^2 + c^2 - a^2))`      =`x^0` = 1.




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