Question

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

• A. x^abc
• B. x^a+b+c
• C. 1
• D.
• E. None of these

Answer 1

The correct option is C

1

$\begin{array}{c}{\left(x^{b-c}\right)}^{\left(b+c\right)}.{\left(x^{a-b}\right)}^{\left(a+b\right)}.{\left(x^{c-a}\right)}^{a+c}\\ =x^{\left(b^2-c^2\right)}.x^{\left(a^2-b^2\right)}.x^{\left(c^2-a^2\right)}\\ =x^{b^2-c^2+a^2-b^2+c^2-a^2}\\ =x^0=1.\end{array}$