Question
Simplify `(x^a/x^b)^(a^2 + b^2 + ab) xx (x^b/x^c)^(b^2 + c^2 + bc) xx (x^c/x^a)^(c^2 + a^2 + ca)`
Answer: Option D
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Sol. Given expression.
=`x^((a - b)(a^2 + b^2 + ab))xx x^((b - c)(b^2 + c^2 + bc)) xx x^((c - a)(c^2 + a^2 + ca))`
=`x^(a^3 - b^3) x^(b^3 - c^3) x^(c^3 - a^3)`
=` x^(a^3 - b^3 + b^3 - c^3 + c^3 - a^3)`
= `x^0` = 1.
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