\(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{a-b}{c-d}\\ \Rightarrow\dfrac{a^{2011}}{c^{2011}}=\dfrac{b^{2011}}{c^{2011}}=\dfrac{a^{2011}+b^{2011}}{c^{2011}+d^{2011}}=\left(\dfrac{a-b}{c-d}\right)^{2011}\)
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