Simplify $\dfrac{(x^{a})^{b} \cdot (x^{b})^{c} \cdot (x^{c})^{a}}{x^{ab} \cdot x^{bc} \cdot x^{ca}}$.

Simplify $\dfrac{(x^{a})^{b} \cdot (x^{b})^{c} \cdot (x^{c})^{a}}{x^{ab} \cdot x^{bc} \cdot x^{ca}}$.
  1. $0$
  2. $1$
  3. $x^{abc}$
  4. $x^{a+b+c}$

Solution

Numerator $= x^{ab + bc + ca}$ and denominator $= x^{ab + bc + ca}$, so the ratio is $x^{0} = 1$.

Asked in: IMO

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