ABC26GN1972 · Surds and Indices
Subject: General Aptitude · Chapter: Surds and Indices · Exam: 2006 · Marks: · Difficulty:
$\left(\frac{x^{a}}{x^{b}}\right)^{(a+b)} \cdot\left(\frac{x^{b}}{x^{c}}\right)^{(b+c)} \cdot\left(\frac{x^{c}}{x^{a}}\right)^{(c+a)}=$ ?
(a)0
(b)$x^{abc}$
(c)$x^{a+b+c}$
(d)1
Answer
Explanation
Given Exp. $=x^{(a-b)(a+b)} \cdot x^{(b-c)(b+c)} \cdot x^{(c-a)(c+a)}$ $$\begin{aligned} & =x^{\left(a^{2}-b^{2}\right)} \cdot x^{\left(b^{2}-c^{2}\right)} \cdot x^{\left(c^{2}-a^{2}\right)} \\ & =x^{\left(a^{2}-b^{2}+b^{2}-c^{2}+c^{2}-a^{2}\right)}=x^{0}=1 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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