Question

16．設(shè)$a={（{\frac{2}{5}}）^{\frac{3}{5}}}$，$b={（{\frac{2}{5}}）^{\frac{2}{5}}}$，$c={（{\frac{3}{5}}）^{\frac{2}{5}}}$，則（　�。�

• A． a＜b＜c
• B． a＜c＜b
• C． b＜c＜a
• D． b＜a＜c

Answer 1

分析 根據(jù)指數(shù)函數(shù)y=${（\frac{2}{5}）}^{x}$單調(diào)性得出${（\frac{2}{5}）}^{\frac{3}{5}}$＜${（\frac{2}{5}）}^{\frac{2}{5}}$，再根據(jù)冪函數(shù)y=${x}^{\frac{2}{5}}$的單調(diào)性得出${（\frac{2}{5}）}^{\frac{2}{5}}$＜${（\frac{3}{5}）}^{\frac{2}{5}}$，即可得出答案．

解答 解：∵指數(shù)函數(shù)y=${（\frac{2}{5}）}^{x}$是定義域R上的減函數(shù)，且$\frac{2}{5}$＜$\frac{3}{5}$，
∴${（\frac{2}{5}）}^{\frac{3}{5}}$＜${（\frac{2}{5}）}^{\frac{2}{5}}$，
即a＜b；
又冪函數(shù)y=${x}^{\frac{2}{5}}$在（0，+∞）上是單調(diào)增函數(shù)，且$\frac{2}{5}$＜$\frac{3}{5}$，
∴${（\frac{2}{5}）}^{\frac{2}{5}}$＜${（\frac{3}{5}）}^{\frac{2}{5}}$，
即b＜c；
∴a＜b＜c．
故選：A．

點評 本題考查了指數(shù)函數(shù)與冪函數(shù)的圖象與性質(zhì)的應(yīng)用問題，是基礎(chǔ)題目．