2018年美国数学大联盟杯五年级竞赛初赛第33题5分
计算：$$\left(2^{2} \times 2^{4} \times 2^{6}\times \ldots ~\times 2^{98} \times 2^{100}\right) \div \left(2^{1} \times 2^{3} \times 2^{5}\times \ldots ~\times 2^{97} \times 2^{99}\right)=$$． 
拓展思维->思想->转化与化归的思想
$$\textasciitilde\textasciitilde\textasciitilde\textasciitilde\left(2^{2} \times 2^{4} \times 2^{6}\times \ldots ~\times 2^{98} \times 2^{100}\right) \div \left(2^{1} \times 2^{3} \times 2^{5}\times \ldots ~\times 2^{97} \times 2^{99}\right)$$  $$=\left( {{2}^{2}}\div {{2}^{1}} \right)\times \left( {{2}^{4}}\div {{2}^{3}} \right)\times \left( {{2}^{6}}\div {{2}^{5}} \right)\times \ldots \times \left( {{2}^{98}}\div {{2}^{97}} \right)\times \left( {{2}^{100}}\div {{2}^{99}} \right)$$  $$=\underbrace{2\times 2\times 2\times \cdots \times 2}_{50个2}$$  $$={{2}^{50}}$$．  故选$$\text{C}$$． 