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计算:(1)$(-2x^{2})\cdot (-2x)^{2}= $____;(2)$(3×10^{2})^{2}×(5×10^{3})= $____.
答案
【易错点睛】(1)$-8x^{4}$ (2)$4.5×10^{8}$
1.(2024湖北中考)计算$2x\cdot 3x^{2}$的结果是()
A.$5x^{2}$
B.$6x^{2}$
C.$5x^{3}$
D.$6x^{3}$
A.$5x^{2}$
B.$6x^{2}$
C.$5x^{3}$
D.$6x^{3}$
答案
1. D
2.下列运算一定正确的是()
A.$2a\cdot 3a= 6a$
B.$3a^{2}\cdot 4a^{3}= 12a^{6}$
C.$(-5a^{3})\cdot 3a= -15a^{4}$
D.$3a^{2}\cdot 3a^{2}= 9a^{2}$
A.$2a\cdot 3a= 6a$
B.$3a^{2}\cdot 4a^{3}= 12a^{6}$
C.$(-5a^{3})\cdot 3a= -15a^{4}$
D.$3a^{2}\cdot 3a^{2}= 9a^{2}$
答案
2. C
3.计算:(1)$3a^{3}\cdot a^{2}= $____; (2)$(-5a^{2}b)\cdot (-3a)= $____;
(3)$(-3x)^{2}\cdot 2x= $____; (4)$3x^{2}\cdot (-2x)^{3}= $____.
(3)$(-3x)^{2}\cdot 2x= $____; (4)$3x^{2}\cdot (-2x)^{3}= $____.
答案
3. (1)$3a^{5}$ (2)$15a^{3}b$ (3)$18x^{3}$ (4)$-24x^{5}$
4.(教材变式)计算:
(1)$2x^{2}\cdot 5x^{5}$; (2)$3ab\cdot 2b^{3}$; (3)$2a^{3}b\cdot 7ab^{2}$;
(4)$4x\cdot (-2x^{2})$; (5)$4xy^{2}\cdot (-\frac {3}{8}x^{2}y)$; (6)$(3×10^{8})×(4×10^{2})$;
(7)$2ab^{2}\cdot (-3ab)^{2}$; (8)$(-2a^{2}b)^{2}\cdot (-3ab^{2})$; (9)$(-3mn^{2})^{3}\cdot (-2m^{2}n)^{2}$.
(1)$2x^{2}\cdot 5x^{5}$; (2)$3ab\cdot 2b^{3}$; (3)$2a^{3}b\cdot 7ab^{2}$;
(4)$4x\cdot (-2x^{2})$; (5)$4xy^{2}\cdot (-\frac {3}{8}x^{2}y)$; (6)$(3×10^{8})×(4×10^{2})$;
(7)$2ab^{2}\cdot (-3ab)^{2}$; (8)$(-2a^{2}b)^{2}\cdot (-3ab^{2})$; (9)$(-3mn^{2})^{3}\cdot (-2m^{2}n)^{2}$.
答案
4. 解：(1)原式$=10x^{7}$；(2)原式$=6ab^{4}$；(3)原式$=14a^{4}b^{3}$；(4)原式$=-8x^{3}$；(5)原式$=-\frac {3}{2}x^{3}y^{3}$；(6)原式$=12×10^{10}=1.2×10^{11}$；(7)原式$=2ab^{2}\cdot 9a^{2}b^{2}=18a^{3}b^{4}$；(8)原式$=4a^{4}b^{2}\cdot (-3ab^{2})=-12a^{5}b^{4}$；(9)原式$=-27m^{3}n^{6}\cdot 4m^{4}n^{2}=-108m^{7}n^{8}$。
5.(教材变式)一种计算机每秒可做$4×10^{8}$次运算,它工作$3×10^{3}$秒运算的次数为____.
答案
5. $1.2×10^{12}$
6.长方体的长是$2×10^{4}cm$,宽是$1.5×10^{3}cm$,高是$3×10^{3}cm$,则它的体积是____$cm^{3}$.
答案
6. $9×10^{10}$
7.如图,四边形$ABCG和四边形CDEF$都是长方形,则它们的面积之和为____(用含$x,y$的式子表示).
答案
7. $\frac {13}{2}xy$
