Question

The value of ${\left(x^{\frac{b+c}{c-a}}\right)}^{\frac{1}{a-b}}{\left(x^{\frac{c+a}{a-b}}\right)}^{\frac{1}{b-c}}{\left(x^{\frac{a+b}{b-c}}\right)}^{\frac{1}{c-a}}$ is

• A. $1$
• B. $a$
• C. $b$
• D. $c$

Answer 1

Answer: (A)

$1$

${\left(x^{\frac{b+c}{c-a}}\right)}^{\frac{1}{a-b}}\times {\left(x^{\frac{c+a}{a-b}}\right)}^{\frac{1}{b-c}}\times {\left(x^{\frac{a+b}{b-c}}\right)}^{\frac{1}{c-a}}$

$\Rightarrow x^{\frac{b+c}{(c-a)(a-b)}}\times x^{\frac{c+a}{(a-b)(b-c)}}\times x^{\frac{a+b}{(b-c)(c-a)}}$

$\Rightarrow x^{\frac{b+c}{(c-a)(a-b)}+\frac{c+a}{(a-b)(b-c)}+\frac{a+b}{(b-c)(c-a)}}$

$\Rightarrow x^{\frac{b^2-c^2+c^2-a^2+a^2-b^2}{(a-b)(b-c)(c-a)}}$

$\Rightarrow x^{\frac{0}{(a-b)(b-c)(c-a)}}$

$\Rightarrow x^0$

$\Rightarrow 1$