Question

State true or false:

$(\frac{x^a}{x^{-b}}{)}^{a^2-ab+b^2}\times (\frac{x^b}{x^{-c}}{)}^{b^2-bc+c^2}\times (\frac{x^c}{x^{-a}}{)}^{c^2-ca+a^2}=$ $x^{2(a^3+b^3+c^3)}$

• A. True
• B. False

Answer 1

The correct option is A True

$(\frac{x^a}{x^{-b}}{)}^{a^2-ab+b^2}\times (\frac{x^b}{x^{-c}}{)}^{b^2-bc+c^2}\times (\frac{x^c}{x^{-a}}{)}^{c^2-ca+a^2}$

$=(x^{a-(-b)}{)}^{a^2-ab+b^2}\times (x^{b-(-c)}{)}^{b^2-bc+c^2}\times (x^{c-(-a)}{)}^{c^2-ca+a^2}$

$=(x^{a+b}{)}^{a^2-ab+b^2}\times (x^{b+c}{)}^{b^2-bc+c^2}\times (x^{c+a}{)}^{c^2-ca+a^2}$

$=\left(x^{a^3+b^3}\right)\times \left(x^{b^3+c^3}\right)\times \left(x^{c^3+a^3}\right)$

$=x^{a^3+b^3+b^3+c^3+c^3+a^3}$

$=x^{2(a^3+b^3+c^3)}$