《2025年阳光课堂金牌练习册八年级数学上册人教版福建专版》

【典型例题】计算：
(1)$9x^{6}y^{2}\cdot (-4x)$；
(2)$(-3y^{3})\cdot (-5x^{3}y^{2})$；
(3)$(4×10^{5})\cdot (5×10^{4})$；
(4)$(-\frac {1}{2}ab^{2}c)^{2}\cdot (-\frac {1}{3}abc^{2})^{3}\cdot (36a^{3}b)$.
思路导引 (1)～(3)直接利用单项式乘单项式的法则计算即可,(4)先进行积的乘方运算,再进行乘法运算.
【解】(1)原式$=[9×(-4)]\cdot (x^{6}\cdot x)y^{2}= -36x^{7}y^{2}$.
(2)原式$=[(-3)×(-5)]\cdot (y^{3}\cdot y^{2})\cdot x^{3}= 15x^{3}y^{5}$.
(3)原式$=(4×5)\cdot (10^{5}×10^{4})= 20×10^{9}= 2×10^{10}$.
(4)原式$=[\frac {1}{4}×(-\frac {1}{27})×36]\cdot (a^{2}\cdot a^{3}\cdot a^{3})\cdot (b^{4}\cdot b^{3}\cdot b)\cdot (c^{2}\cdot c^{6})= -\frac {1}{3}a^{8}b^{8}c^{8}$.
规律方法 单项式乘单项式的计算步骤：

答案：
(1)
$9x^{6}y^{2}\cdot (-4x)=[9×(-4)](x^{6}\cdot x)y^{2}=-36x^{7}y^{2}$
(2)
$(-3y^{3})\cdot (-5x^{3}y^{2})=[(-3)×(-5)]x^{3}(y^{3}\cdot y^{2}) = 15x^{3}y^{5}$
(3)
$(4×10^{5})\cdot (5×10^{4})=(4×5)(10^{5}×10^{4}) = 20×10^{9}=2×10^{10}$
(4)
$(-\frac{1}{2}ab^{2}c)^{2}\cdot (-\frac{1}{3}abc^{2})^{3}\cdot (36a^{3}b)$
$=(\frac{1}{4}a^{2}b^{4}c^{2})\cdot (-\frac{1}{27}a^{3}b^{3}c^{6})\cdot (36a^{3}b)$
$=[\frac{1}{4}×(-\frac{1}{27})×36](a^{2}\cdot a^{3}\cdot a^{3})(b^{4}\cdot b^{3}\cdot b)(c^{2}\cdot c^{6})$
$=-\frac{1}{3}a^{8}b^{8}c^{8}$

1. 计算：$6xy^{2}\cdot (-\frac {1}{2}x^{3}y^{3})=$(B)
A.$3x^{4}y^{5}$
B.$-3x^{4}y^{5}$
C.$3x^{3}y^{6}$
D.$-3x^{3}y^{6}$

答案： B

2. 计算：
(1)$3x^{2}y\cdot (-2xy^{3})$；
(2)$(-5a^{2}b^{3})\cdot (-4b^{2}c)$；
(3)$(-3m^{6}n)\cdot (2mn^{2})$；
(4)$(-5a^{2}b)\cdot (-3a)$；
(5)$(2a)^{3}\cdot (-5a^{2}b)$；
(6)$(-2ab)^{3}\cdot (-3ab)^{2}$.

答案：
(1)
$3x^{2}y\cdot (-2xy^{3})$
$=[3×(-2)]\cdot(x^{2}\cdot x)\cdot(y\cdot y^{3})$
$=-6x^{3}y^{4}$
(2)
$(-5a^{2}b^{3})\cdot (-4b^{2}c)$
$=[(-5)×(-4)]\cdot(a^{2})\cdot(b^{3}\cdot b^{2})\cdot c$
$=20a^{2}b^{5}c$
(3)
$(-3m^{6}n)\cdot (2mn^{2})$
$=[(-3)×2]\cdot(m^{6}\cdot m)\cdot(n\cdot n^{2})$
$=-6m^{7}n^{3}$
(4)
$(-5a^{2}b)\cdot (-3a)$
$=[(-5)×(-3)]\cdot(a^{2}\cdot a)\cdot b$
$=15a^{3}b$
(5)
$(2a)^{3}\cdot (-5a^{2}b)$
$=(8a^{3})\cdot (-5a^{2}b)$
$=[8×(-5)]\cdot(a^{3}\cdot a^{2})\cdot b$
$=-40a^{5}b$
(6)
$(-2ab)^{3}\cdot (-3ab)^{2}$
$=(-8a^{3}b^{3})\cdot (9a^{2}b^{2})$
$=[(-8)×9]\cdot(a^{3}\cdot a^{2})\cdot(b^{3}\cdot b^{2})$
$=-72a^{5}b^{5}$