Simplify $\left(\dfrac{x^{-2} y^{3}}{x^{4} y^{-1}}\right)^{-2}$.

Simplify $\left(\dfrac{x^{-2} y^{3}}{x^{4} y^{-1}}\right)^{-2}$.
  1. $\dfrac{x^{12}}{y^{8}}$
  2. $\dfrac{y^{8}}{x^{12}}$
  3. $x^{4} y^{-4}$
  4. $\dfrac{1}{x^{12} y^{8}}$

Solution

Inside: $x^{-2-4} y^{3-(-1)} = x^{-6} y^{4}$. Raise to $-2$: $x^{12} y^{-8} = \dfrac{x^{12}}{y^{8}}$.

Asked in: IMO

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