Surds and Indices

x^b ^{(b + c - a)} . x^c ^{(c + a - b)} . x^a ^{(a + b - c)} = ?

x^c x^a x^b

A x^abc

B 1

C x^{ab + bc + ca}

D x^{a + b + c}

ANS:B - 1

Given Exp.

= x^{(b - c)(b + c - a)} . x^{(c - a)(c + a - b)} . x^{(a - b)(a + b - c)}

= x^{(b - c)(b + c) - a(b - c)} . x^{(c - a)(c + a) - b(c - a)}
. x^{(a - b)(a + b) - c(a - b)}

= x^{(b² - c² + c² - a² + a² - b²)} . x^{-a(b - c) - b(c - a) - c(a - b)}

= (x⁰ x x⁰)

= (1 x 1) = 1.

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