\(ac=bd\Rightarrow\frac{a}{d}=\frac{b}{c}\Rightarrow\frac{a}{b}=\frac{d}{c}=\frac{a^{2000}}{b^{2000}}=\frac{d^{2000}}{c^{2000}}=\left(\frac{a}{b}\right)^{2000}=\left(\frac{c}{d}\right)^{2000}=\frac{\left(a+d\right)^{2000}}{\left(b+c\right)^{2000}}\)
\(=\frac{a^{2000}+d^{2000}}{b^{2000}+c^{2000}}\)
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