Question

17．已知-0.5x^a+by^a-b与$\frac{2}{3}{x}^{a-1}{y}^{3}$是同类项，那么（　　）

• A． $\left\{\begin{array}{l}{a=-1}\\{b=2}\end{array}\right.$
• B． $\left\{\begin{array}{l}{a=1}\\{b=-2}\end{array}\right.$
• C． $\left\{\begin{array}{l}{a=-2}\\{b=1}\end{array}\right.$
• D． $\left\{\begin{array}{l}{a=2}\\{b=-1}\end{array}\right.$

Answer 1

分析 根据同类项是字母相同且相同字母的指数也相同，可得答案．

解答 解：由-0.5x^a+by^a-b与$\frac{2}{3}{x}^{a-1}{y}^{3}$是同类项，得
$\left\{\begin{array}{l}{a+b=a-1}\\{a-b=3}\end{array}\right.$，
解得$\left\{\begin{array}{l}{a=2}\\{b=-1}\end{array}\right.$．
故选：D．

点评 本题考查了同类项，利用同类项的定义得出方程组是解题关键．