Question

The value of ${\left(\frac{x^a}{x^b}\right)}^{a^2+ab+b^2}\cdot {\left(\frac{x^b}{x^c}\right)}^{b^2+bc+c^2}\cdot {\left(\frac{x^c}{x^a}\right)}^{c^2+ca+b^2}$.

• A. $-1$
• B. $x^{abc}$
• C. $1$
• D. $x(a+b+c)$

Answer 1

The correct option is C $1$

$(x^{a-b}{)}^{a^2+ab+b^2}\cdot (x^{b-c}{)}^{b^2+bc+c^2}\cdot (x^{c-a}{)}^{c^2+ca+a^2}$
$\Rightarrow x^{a^3-b^3}\cdot x^{b^3-c^3}\cdot x^{c^3-a^3}=x^0=1$.