Question

${\left(\frac{x^b}{x^c}\right)}^{\left(b+c-a\right)}.{\left(\frac{x^c}{x^a}\right)}^{\left(c+a-b\right)}.{\left(\frac{x^a}{x^b}\right)}^{\left(a+b-c\right)}=?$

• A. x^abc
• B. 1
• C. x^ab+bc+ca
• D. x^a+b+c
• E. 0

Answer 1

The correct option is B

1

On multiplying the powers and adding them,
(b-c)(b+c-a) + (c-a)(c+a-b) + (a-b)(a+b-c)

= $b^2$+bc-ab-bc-$c^2$+ac +$c^2$+ac-bc-ac-$a^2$+ab +$a^2$+ab-ac-ab-$b^2$+bc

= 0

So, $x^{(b-c)(b+c-a)+(c-a)(c+a-b)+(a-b)(a+b-c)}$ = $x^0$ = 1