Surds and Indices - Arithmetic Aptitude Questions and Answers

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$[\frac { X^b } {X^c } ]^(b+c-a)$ . $[\frac { X^c } {X^a} ]^(c+a-b)$ $[\frac { X^a} {X^b} ]^(a+b-c)=?$

x^abc

x^{ab + bc + ca}

x^{a + b + c}

Answer : Option B

Explanation :

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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