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1. 计算$(3a^6)÷a$的结果是（
A.$3a^6$
B.$2a^5$
C.$2a^6$
D.$3a^5$
D
）A.$3a^6$
B.$2a^5$
C.$2a^6$
D.$3a^5$
答案
1.D
2. 计算$(-2a^3)^2 ÷ a^2$的结果是(
A.$-2a^3$
B.$4a^4$
C.$4a^3$
D.$-2a^4$
B
)A.$-2a^3$
B.$4a^4$
C.$4a^3$
D.$-2a^4$
答案
2.B
3.若一个长方形的面积为$a^2bc$，长为$\frac{1}{5}ac$，则它的宽为
5ab
。答案
3.5ab
4.计算:
(1)$(3a^2b^3c^4)^2 ÷ (-\dfrac{1}{3}a^2b^4)$;
(2)$(-2x^2y^3) ÷ (-\dfrac{1}{2}xy^2) · 2xy$.
(1)$(3a^2b^3c^4)^2 ÷ (-\dfrac{1}{3}a^2b^4)$;
(2)$(-2x^2y^3) ÷ (-\dfrac{1}{2}xy^2) · 2xy$.
答案
4. 解:(1)原式$=9a^4b^6c^8 ÷ (-\dfrac{1}{3}a^2b^4) =-27a^2b^2c^8$.
(2)原式$=[(-2) ÷ (-\dfrac{1}{2}) × 2]x^{2-1+1} · y^{3-2+1} =8x^2y^2$.
(2)原式$=[(-2) ÷ (-\dfrac{1}{2}) × 2]x^{2-1+1} · y^{3-2+1} =8x^2y^2$.
1. 如果$(8a^{3}b^{m})÷(8a^{n}b^{2})=b^{2}$，那么$m$，$n$的值分别为（
A.$4,3$
B.$4,1$
C.$1,3$
D.$2,3$
A
）A.$4,3$
B.$4,1$
C.$1,3$
D.$2,3$
答案
1.A
2.先化简，再求值：$\frac{1}{3}a^2b^3 · (3ab^2)^2 ÷ [6(a^2b^3)^2]$，其中$a=2025$，$b=-2.$
答案
2. 解:原式$=\dfrac{1}{3}a^2b^3 · 9a^2b^4 ÷ (6a^4b^6) =3a^4b^7 ÷ (6a^4b^6) =\dfrac{1}{2}b$.
当$b=-2$时,原式$=\dfrac{1}{2}×(-2)=-1$.
当$b=-2$时,原式$=\dfrac{1}{2}×(-2)=-1$.
已知$(a-2)^2 + (b+2)^2 + (c-3)^2 = 0$，求$\frac{1}{3}a^2b^3c^4 · (3ab^2c^2)^2 ÷ 6(a^2b^3c^4)^2$的值。
答案
解:$\because (a-2)^2+(b+2)^2+(c-3)^2=0$,
$\therefore a-2=0,b+2=0,c-3=0$,
$\therefore a=2,b=-2,c=3$.
$\therefore \dfrac{1}{3} a^2b^3c^4 · (3ab^2c^2)^2 ÷ 6 (a^2b^3c^4)^2 = \dfrac{1}{3}a^2b^3c^4 · 9a^2b^4c^4 ÷ 6a^4b^6c^8=\dfrac{1}{2}b=-1$.
$\therefore a-2=0,b+2=0,c-3=0$,
$\therefore a=2,b=-2,c=3$.
$\therefore \dfrac{1}{3} a^2b^3c^4 · (3ab^2c^2)^2 ÷ 6 (a^2b^3c^4)^2 = \dfrac{1}{3}a^2b^3c^4 · 9a^2b^4c^4 ÷ 6a^4b^6c^8=\dfrac{1}{2}b=-1$.
