1. 计算$(\frac{a^3}{4b})^2$的结果是()
A.$\frac{a^6}{4b}$
B.$\frac{a^6}{16b^2}$
C.$\frac{a^5}{8b^2}$
D.$\frac{a^5}{4b}$

B

$(\frac{a^3}{4b})^2=\frac{(a^3)^2}{(4b)^2}=\frac{a^{3×2}}{4^2b^2}=\frac{a^6}{16b^2}$，结果为选项B。

2. 计算:$\frac{y}{x} ÷ \frac{y}{2} \cdot \frac{2}{y}$的结果是()
A.$\frac{4}{xy}$
B.$\frac{1}{2}x$
C.$\frac{y}{x}$
D.$2y$

A

$\frac{y}{x} ÷ \frac{y}{2} \cdot \frac{2}{y}$
$=\frac{y}{x} \cdot \frac{2}{y} \cdot \frac{2}{y}$
$=\frac{2}{x} \cdot \frac{2}{y}$
$=\frac{4}{xy}$
A

3. 计算:$(-\frac{a}{b})^2 ÷ (-a^4b) = $.

-$\frac{1}{a^{2}b^{3}}$

$(-\frac{a}{b})^2 ÷ (-a^4b)$
$=\frac{a^2}{b^2}÷(-a^4b)$
$=\frac{a^2}{b^2}×(-\frac{1}{a^4b})$
$=-\frac{1}{a^{2}b^{3}}$

题型 1 下列计算中,错误的是()
A.$(\frac{2y}{-x^2})^3 = -\frac{8y^3}{x^6}$
B.$(\frac{4b^3}{-3c^2})^2 = \frac{16b^6}{9c^4}$
C.$(\frac{x + y}{x - y})^2 = \frac{x^2 + y^2}{x^2 - y^2}$
D.$(-\frac{b^2}{a^3})^{2n} = \frac{b^{4n}}{a^{6n}}$

C

题型 2 计算:(1)$(\frac{-2y}{-x})^2$;
(2)$(\frac{-2a^2b^4}{5c^3})^3$;(3)$\frac{a - a^2}{a^2 - 1} ÷ \frac{a}{a - 1} \cdot (\frac{a + 1}{a - 1})^2$.
方法归纳交流 分式的乘除、乘方混合运算顺序:先,再.运算结果要化为.
解:
(1)$(\frac{-2y}{-x})^{2}=\frac{4y^{2}}{x^{2}}$.
(2)$(\frac{-2a^{2}b^{4}}{5c^{3}})^{3}=-\frac{8a^{6}b^{12}}{125c^{9}}$.
(3)$\frac{a-a^{2}}{a^{2}-1}÷\frac{a}{a-1}\cdot(\frac{a+1}{a-1})^{2}=\frac{a(1-a)}{(a+1)(a-1)}\cdot\frac{a-1}{a}\cdot\frac{(a+1)^{2}}{(a-1)^{2}}=-\frac{a+1}{a-1}$.

解:
(1)$(\frac{-2y}{-x})^{2}=\frac{4y^{2}}{x^{2}}$.
(2)$(\frac{-2a^{2}b^{4}}{5c^{3}})^{3}=-\frac{8a^{6}b^{12}}{125c^{9}}$.
(3)$\frac{a-a^{2}}{a^{2}-1}÷\frac{a}{a-1}\cdot(\frac{a+1}{a-1})^{2}=\frac{a(1-a)}{(a+1)(a-1)}\cdot\frac{a-1}{a}\cdot\frac{(a+1)^{2}}{(a-1)^{2}}=-\frac{a+1}{a-1}$. 方法归纳交流 乘方 乘除 最简分式