Question

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

• A. $-1$
• B. 1
• C. 2
• D. $-2$

Answer 1

The correct option is B 1

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

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

$=$ $x^{a^2-b^2}\times x^{b^2-c^2}\times x^{c^2-a^2}$

$=$ $x^{a^2-b^2+b^2-c^2+c^2-a^2}$

$=$ $x^0$

$=$ $1$

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