1. 化简$\left(-\frac{3y}{x}\right)^2$的结果是()
A.$\frac{3y^2}{x^2}$
B.$\frac{9y^2}{x^2}$
C.$\frac{6y^2}{x^2}$
D.$-\frac{9y^2}{x^2}$

B

$\left(-\frac{3y}{x}\right)^2=\frac{( -3y)^2}{x^2}=\frac{9y^2}{x^2}$，答案选B。

2. 化简$x^3\left(\frac{y^3}{x}\right)^2$的结果是( )

A.$xy^6$
B.$xy^5$
C.$x^2y^5$
D.$x^2y^6$

A

$x^3\left(\frac{y^3}{x}\right)^2 = x^3 \cdot \frac{y^6}{x^2} = x y^6$
A

3. 计算$\frac{x^2}{y}÷\left(-\frac{y}{x}\right)\cdot\left(\frac{y}{x}\right)^2$的结果是()
A.$-x$
B.$-\frac{x^2}{y}$
C.$\frac{x}{y}$
D.$\frac{x^2}{y}$

A

解：$\begin{aligned}\frac{x^2}{y}÷\left(-\frac{y}{x}\right)\cdot\left(\frac{y}{x}\right)^2&=\frac{x^2}{y}×\left(-\frac{x}{y}\right)\cdot\frac{y^2}{x^2}\\&=-\frac{x^3}{y^2}\cdot\frac{y^2}{x^2}\\&=-x\end{aligned}$
A

4. 有下列各式:①$\left(\frac{-2mn}{a^2b}\right)^2$;②$-\frac{8m^4n^2}{a^5b}\cdot\frac{an}{bm^2}$;③$\left(\frac{2m}{-ab^2}\right)^2\cdot\left(\frac{bn}{a}\right)^2$;④$\frac{2mn^2}{ab^2}÷\frac{a^3}{m}$.其中计算结果相等的是()
A.①②
B.②③
C.①③
D.③④

C

①$\left(\frac{-2mn}{a^2b}\right)^2=\frac{4m^2n^2}{a^4b^2}$；
②$-\frac{8m^4n^2}{a^5b}\cdot\frac{an}{bm^2}=-\frac{8m^2n^3}{a^4b^2}$；
③$\left(\frac{2m}{-ab^2}\right)^2\cdot\left(\frac{bn}{a}\right)^2=\frac{4m^2}{a^2b^4}\cdot\frac{b^2n^2}{a^2}=\frac{4m^2n^2}{a^4b^2}$；
④$\frac{2mn^2}{ab^2}÷\frac{a^3}{m}=\frac{2mn^2}{ab^2}\cdot\frac{m}{a^3}=\frac{2m^2n^2}{a^4b^2}$。
计算结果相等的是①③。
C

5. 计算:$\left(\frac{-2a^2b}{3c}\right)^2= $.

$\frac{4a^4b^2}{9c^2}$

$\left(\frac{-2a^2b}{3c}\right)^2=\frac{(-2)^2(a^2)^2b^2}{3^2c^2}=\frac{4a^4b^2}{9c^2}$

6. 计算:$\left(-\frac{y}{2x}\right)^3÷\frac{y^2}{4x}= $.

$-\frac{y}{2x^2}$

$\begin{aligned}\left(-\frac{y}{2x}\right)^3÷\frac{y^2}{4x}&=-\frac{y^3}{8x^3}×\frac{4x}{y^2}\\&=-\frac{4xy^3}{8x^3y^2}\\&=-\frac{y}{2x^2}\end{aligned}$
$-\frac{y}{2x^2}$