Question

1．计算：（$\frac{1}{2}$）²÷（$\frac{2}{3}$）²÷（$\frac{3}{4}$）²÷（$\frac{4}{5}$）²÷（$\frac{5}{6}$）²÷（$\frac{6}{7}$）²÷（$\frac{7}{8}$）²÷（$\frac{8}{9}$）²÷（$\frac{9}{10}$）²．

Answer 1

分析 先计算有理数的乘方，再计算有理数的除法．

解答 解：原式=$\frac{1}{4}$÷$\frac{4}{9}$$÷\frac{9}{16}÷\frac{16}{25}÷\frac{25}{36}÷\frac{36}{49}÷\frac{49}{64}÷\frac{64}{81}÷\frac{81}{100}$
=$\frac{1}{4}×\frac{9}{4}×\frac{16}{9}×\frac{25}{16}×\frac{36}{25}×\frac{49}{36}×\frac{64}{49}×\frac{81}{64}×\frac{100}{81}$
=$\frac{25}{8}$．

点评 本题考查了有理数的除法，解决本题的关键是熟记除以一个数等于乘以这个数的倒数．