Question

The value of ${\left(\frac{x^a}{x^b}\right)}^{(a+b)}\times {\left(\frac{x^b}{x^c}\right)}^{(b+c)}\times {\left(\frac{x^c}{x^a}\right)}^{(c+a)}$ is equal to

• A. 1
• B. 0
• C. $x^{abc}$
• D. abc

Answer 1

The correct option is A 1

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

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

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

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

$=x^{\left(0\right)}=1$