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1. [2024长沙模拟]计算$\frac{y}{x} ÷ \frac{y}{2} · \frac{2}{y}$的结果是（
A.$\frac{4}{xy}$
B.$\frac{1}{2}x$
C.$\frac{y}{x}$
D.$2y$
A
）A.$\frac{4}{xy}$
B.$\frac{1}{2}x$
C.$\frac{y}{x}$
D.$2y$
答案
1. A
2. 计算:
(1) $\frac{3b^2}{16a} ÷ \frac{bc}{2a^2} · (-\frac{2a}{b});$
(2) $\frac{a+2}{a^2 -1} · \frac{a-1}{a^2 +4a +4} ÷ \frac{1}{a+2};$
(3) $\frac{1}{x-1} ÷ (x+2) · \frac{x-1}{x+2}.$
(1) $\frac{3b^2}{16a} ÷ \frac{bc}{2a^2} · (-\frac{2a}{b});$
(2) $\frac{a+2}{a^2 -1} · \frac{a-1}{a^2 +4a +4} ÷ \frac{1}{a+2};$
(3) $\frac{1}{x-1} ÷ (x+2) · \frac{x-1}{x+2}.$
答案
(1) $-\frac{3a^2}{4c}$
(2) $\frac{1}{a+1}$
(3) $\frac{1}{(x+2)^2}$
(2) $\frac{1}{a+1}$
(3) $\frac{1}{(x+2)^2}$
3. 下列计算中，错误的是 $( )$
A.$( \dfrac{3y}{-x^2} )^3 = -\dfrac{-9y^3}{x^6}$
B.$( \dfrac{4b^3}{-3c^2} )^2 = \dfrac{16b^6}{9c^4}$
C.$( \dfrac{5x^3y^2}{-2z} )^2 = \dfrac{25x^6y^4}{4z^2}$
D.$( \dfrac{b^2}{-a^3} )^2 = \dfrac{b^4}{a^6}$
A.$( \dfrac{3y}{-x^2} )^3 = -\dfrac{-9y^3}{x^6}$
B.$( \dfrac{4b^3}{-3c^2} )^2 = \dfrac{16b^6}{9c^4}$
C.$( \dfrac{5x^3y^2}{-2z} )^2 = \dfrac{25x^6y^4}{4z^2}$
D.$( \dfrac{b^2}{-a^3} )^2 = \dfrac{b^4}{a^6}$
答案
3. A
4. 计算：
(1) $(-\dfrac{m^3}{n})^2 =$
(2) $(\dfrac{ab^2}{c^2})^3 =$
(1) $(-\dfrac{m^3}{n})^2 =$
$\frac{m^6}{n^2}$
；(2) $(\dfrac{ab^2}{c^2})^3 =$
$\frac{a^3b^6}{c^6}$
。答案
(1) $\frac{m^6}{n^2}$
(2) $\frac{a^3b^6}{c^6}$
(2) $\frac{a^3b^6}{c^6}$
5. [2023河北]化简 $ x^3 · ( \frac{y^3}{x} )^2 $ 的结果是
$xy^6$
。答案
$xy^6$
6. 计算:
(1) $(\dfrac{5y^2 z}{-2x^2})^3 =$
(2) $(\dfrac{-4a}{a - b})^2 =$
(3) $(-\dfrac{y}{x^2})^3 ÷ (\dfrac{y^2}{x^3} · \dfrac{x^2}{y}) =$
(4) $(\dfrac{-xy}{z})^3 · (-\dfrac{xz}{y}) ÷ (\dfrac{yz}{-x})^2 =$
(1) $(\dfrac{5y^2 z}{-2x^2})^3 =$
$-\frac{125y^6z^3}{8x^6}$
;(2) $(\dfrac{-4a}{a - b})^2 =$
$\frac{16a^2}{(a-b)^2}$
;(3) $(-\dfrac{y}{x^2})^3 ÷ (\dfrac{y^2}{x^3} · \dfrac{x^2}{y}) =$
$-\frac{y^2}{x^5}$
;(4) $(\dfrac{-xy}{z})^3 · (-\dfrac{xz}{y}) ÷ (\dfrac{yz}{-x})^2 =$
$\frac{x^6}{z^4}$
.答案
(1) $-\frac{125y^6z^3}{8x^6}$
(2) $\frac{16a^2}{(a-b)^2}$
(3) $-\frac{y^2}{x^5}$
(4) $\frac{x^6}{z^4}$
(2) $\frac{16a^2}{(a-b)^2}$
(3) $-\frac{y^2}{x^5}$
(4) $\frac{x^6}{z^4}$
7. 计算:
(1)$(\dfrac{4x}{3y})^2 ÷ \dfrac{4x}{y} · \dfrac{y^2}{4x^2} ÷ (-\dfrac{x}{y})^2$；
(2)$(\dfrac{-a}{b})^2 ÷ (\dfrac{2a^2}{5b})^2 · \dfrac{a}{5b}$。
(1)$(\dfrac{4x}{3y})^2 ÷ \dfrac{4x}{y} · \dfrac{y^2}{4x^2} ÷ (-\dfrac{x}{y})^2$；
(2)$(\dfrac{-a}{b})^2 ÷ (\dfrac{2a^2}{5b})^2 · \dfrac{a}{5b}$。
答案
(1) $\frac{y^3}{9x^3}$
(2) $\frac{5}{4ab}$
(2) $\frac{5}{4ab}$
8.若$x+y=5$，则$(-\dfrac{x^2 - y^2}{2xy})^2 ÷ (\dfrac{x - y}{-xy})^2$的值为
$\frac{25}{4}$
。答案
$\frac{25}{4}$
