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1. 下列各式的计算结果与$x^2 · x^3$相等的是(
A.$x^3 + x^3$
B.$x^7 - x^2$
C.$(x^2)^3$
D.$x^7 ÷ x^2$
D
).A.$x^3 + x^3$
B.$x^7 - x^2$
C.$(x^2)^3$
D.$x^7 ÷ x^2$
答案
1. D
2. 下列运算正确的是(
A.$m^2 · m^3 = m^5$
B.$m^6 ÷ m^2 = m^3$
C.$2m + 3n = 5mn$
D.$(m^2)^3 = m^5$
A
).A.$m^2 · m^3 = m^5$
B.$m^6 ÷ m^2 = m^3$
C.$2m + 3n = 5mn$
D.$(m^2)^3 = m^5$
答案
2. A
3. 下列选项的括号内填入$a^2$,等式成立的是(
A.$a^2 + (\quad) = a^5$
B.$a^8 ÷ (\quad) = a^4$
C.$(\quad)^3 = a^8$
D.$a^3 · (\quad) = a^5$
D
).A.$a^2 + (\quad) = a^5$
B.$a^8 ÷ (\quad) = a^4$
C.$(\quad)^3 = a^8$
D.$a^3 · (\quad) = a^5$
答案
3. D
4. 下列计算结果为$a^5$的是(
A.$(a^2)^3$
B.$a^{10} ÷ a^2$
C.$a^3 + a^2$
D.$a^2 · a^3$
D
).A.$(a^2)^3$
B.$a^{10} ÷ a^2$
C.$a^3 + a^2$
D.$a^2 · a^3$
答案
4. D
5. 已知$m - n = 4$（$m$、$n$是正整数），则$2^m ÷ 2^n =$
16
答案
5. 16
6. 判断下列计算是否正确,错误的给予纠正:
(1) $a^3 ÷ a = a^3$.
(2) $a^5 ÷ b^2 = a^3 b$.
(3) $(a-b)^6 ÷ (a-b)^2 = (a-b)^3$.
(4) $(-m)^7 ÷ (-m)^2 = m^5$.
(1) $a^3 ÷ a = a^3$.
(2) $a^5 ÷ b^2 = a^3 b$.
(3) $(a-b)^6 ÷ (a-b)^2 = (a-b)^3$.
(4) $(-m)^7 ÷ (-m)^2 = m^5$.
答案
(1)错误,$a^3 ÷ a = a^2$.
(2)错误,$a^5$与$b^2$不是同底数幂,指数不能相减.
(3)错误,$(a-b)^6 ÷ (a-b)^2 = (a-b)^4$.
(4)错误,$(-m)^7 ÷ (-m)^2 = -m^5$.
(2)错误,$a^5$与$b^2$不是同底数幂,指数不能相减.
(3)错误,$(a-b)^6 ÷ (a-b)^2 = (a-b)^4$.
(4)错误,$(-m)^7 ÷ (-m)^2 = -m^5$.
7. 计算：
(1) $a^2 · a^4 + (a^3)^2 - a^8 ÷ a^2$
(2) $(-a)^2 + a^7 ÷ a - (a^2)^3$
(3) $y^4 + (y^2)^4 ÷ y^4 - (-y^2)^2$
(4) $a^{12} ÷ a^3 · a^4$
(1) $a^2 · a^4 + (a^3)^2 - a^8 ÷ a^2$
(2) $(-a)^2 + a^7 ÷ a - (a^2)^3$
(3) $y^4 + (y^2)^4 ÷ y^4 - (-y^2)^2$
(4) $a^{12} ÷ a^3 · a^4$
答案
(1)原式=$a^6 + a^6 - a^6 = a^6$.
(2)原式=$a^2 + a^6 - a^6 = a^2$.
(3)原式=$y^4 + y^8 ÷ y^4 - y^4 = y^4 + y^4 - y^4 = y^4$.
(4)原式=$a^9 · a^4 = a^{13}$.
(2)原式=$a^2 + a^6 - a^6 = a^2$.
(3)原式=$y^4 + y^8 ÷ y^4 - y^4 = y^4 + y^4 - y^4 = y^4$.
(4)原式=$a^9 · a^4 = a^{13}$.
