Question

20．（$\frac{21}{4}$）^-6×（$\frac{21}{8}$）⁵÷2^-3．

Answer 1

分析 根據(jù)負整數(shù)指數(shù)冪與正整數(shù)指數(shù)冪互為倒數(shù)，可得積的乘方，根據(jù)積的乘方，可得答案．

解答 解：原式=（$\frac{4}{21}$）⁶×（$\frac{21}{8}$）⁵÷$\frac{1}{{2}^{3}}$
=（$\frac{4}{21}$）⁵×（$\frac{21}{8}$）⁵×$\frac{4}{21}$÷$\frac{1}{8}$
=（$\frac{4}{21}$×$\frac{21}{8}$）⁵×$\frac{4}{21}$×8
=（$\frac{1}{2}$）⁵×$\frac{32}{21}$
=$\frac{1}{21}$．

點評 本題考查了負整數(shù)指數(shù)冪，利用了負整數(shù)指數(shù)冪與正整數(shù)指數(shù)冪互為倒數(shù)，積的乘方．