Question

Prove that(x^a/x^b)^c * (x^b/x^c)^a * (x^c/x^a)^b=1 Please answer it fast!!!!!! I will mark you brainliest

Answer 1

To prove :-

$\displaystyle{\sf{(\frac{x^a}{x^b})^c \times (\frac{x^b}{x^c})^a \times (\frac{x^c}{x^a})^b=1 }}$

Proof :-

LHS :-

$\displaystyle{\sf{(\frac{x^a}{x^b})^c \times (\frac{x^b}{x^c})^a \times (\frac{x^c}{x^a})^b }}\\\\\displaystyle{\sf{=(\frac{x^a^c}{x^b^c}) \times (\frac{x^b^a}{x^c^a}) \times (\frac{x^c^b}{x^a^b}) }}\\\\\displaystyle{\sf{=(x^{ac-bc}) \times (x^{ba-ca}) \times (x^{cb-ab}) }}} \\\\\displaystyle{\sf{=x^{ac-bc+(ba-ca)+(bc-ab)}}}\\\\\displaystyle{\sf{= x^{ab-bc+ab-ac+bc-ab}}}\\\\\displaystyle{\sf{= x^0}}\\\\\displaystyle{\sf{= 1=RHS}}$

◘ ◙ Thus proved ◙ ◘