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1. 化简 $ x^3 · ( \frac{y^3}{x} )^2 $ 的结果是（
A.$ xy^6 $
B.$ xy^5 $
C.$ x^2y^5 $
D.$ x^2y^6 $
A
）A.$ xy^6 $
B.$ xy^5 $
C.$ x^2y^5 $
D.$ x^2y^6 $
答案
A
2.计算 $a^2 ÷ \frac{1}{b} · b$ 的结果是(
A.$a^2$
B.$\frac{a^2}{b^2}$
C.$a^2b^2$
D.$2a^2b^2$
C
)A.$a^2$
B.$\frac{a^2}{b^2}$
C.$a^2b^2$
D.$2a^2b^2$
答案
C
3. 下列式子计算后的结果与$\frac{1}{a^3}$相等的是（
A.$a÷(\frac{1}{a^2}× a^2)$
B.$a÷(\frac{1}{a^2}÷ a^2)$
C.$a÷\frac{1}{a}× a^2$
D.$a×\frac{1}{a^2}÷ a^2$
D
）A.$a÷(\frac{1}{a^2}× a^2)$
B.$a÷(\frac{1}{a^2}÷ a^2)$
C.$a÷\frac{1}{a}× a^2$
D.$a×\frac{1}{a^2}÷ a^2$
答案
D
4. 下列计算正确的是（
A.$(\dfrac{1}{a - b})^2 = \dfrac{1}{a^2 - b^2}$
B.$(\dfrac{x^2}{4})^2 = \dfrac{x^4}{8}$
C.$(-\dfrac{1}{2a^3})^2 = \dfrac{1}{4a^6}$
D.$(-\dfrac{3x}{y})^2 = \dfrac{3x^2}{y^2}$
C
）A.$(\dfrac{1}{a - b})^2 = \dfrac{1}{a^2 - b^2}$
B.$(\dfrac{x^2}{4})^2 = \dfrac{x^4}{8}$
C.$(-\dfrac{1}{2a^3})^2 = \dfrac{1}{4a^6}$
D.$(-\dfrac{3x}{y})^2 = \dfrac{3x^2}{y^2}$
答案
C
5.计算$a^2 ÷ b · \frac{1}{b} ÷ c · \frac{1}{c} ÷ d · \frac{1}{d}$等于（
A.$a^2$
B.$\frac{a^2}{bcd}$
C.$\frac{a^2}{b^2 c^2 d^2}$
D.$\frac{a^2}{b^2 c^2}$
C
）A.$a^2$
B.$\frac{a^2}{bcd}$
C.$\frac{a^2}{b^2 c^2 d^2}$
D.$\frac{a^2}{b^2 c^2}$
答案
C 点拨: 原式=$a^2 · \frac{1}{b} · \frac{1}{b} · \frac{1}{c} · \frac{1}{c} · \frac{1}{d} · \frac{1}{d} =\frac{a^2}{b^2 c^2 d^2}$
6.计算：
(1)$(\dfrac{2y}{x})^2 · \dfrac{x}{4y^3} =$
(2)$(\dfrac{a-b}{ab})^3 · (\dfrac{ab}{a-b})^2 ÷ (a-b)^2 =$
(1)$(\dfrac{2y}{x})^2 · \dfrac{x}{4y^3} =$
$\frac{1}{xy}$
；(2)$(\dfrac{a-b}{ab})^3 · (\dfrac{ab}{a-b})^2 ÷ (a-b)^2 =$
$\frac{1}{a^2b - ab^2}$
。答案
(1)$\frac{1}{xy}$
(2)$\frac{1}{a^2b - ab^2}$
(2)$\frac{1}{a^2b - ab^2}$
7.计算：
(1)$(\dfrac{2xy^3}{z^2})^2÷\dfrac{6x^2}{y^3}$；
(2)$-(\dfrac{m}{n})^2·(-\dfrac{n^2}{m})^4÷(-mn^4)$。
(1)$(\dfrac{2xy^3}{z^2})^2÷\dfrac{6x^2}{y^3}$；
(2)$-(\dfrac{m}{n})^2·(-\dfrac{n^2}{m})^4÷(-mn^4)$。
答案
解:(1)原式=$\frac{4x^2 y^6}{z^4} · \frac{y^3}{6x^2} =\frac{2y^9}{3z^4}$.
(2)原式=$\frac{m^2}{n^2} · \frac{n^8}{m^4} · \frac{1}{mn^4} =\frac{n^2}{m^3}$.
(2)原式=$\frac{m^2}{n^2} · \frac{n^8}{m^4} · \frac{1}{mn^4} =\frac{n^2}{m^3}$.
