[例1]计算:
(1)a7÷a4;
(2)(−m)10÷(−m)7;
(3)(xy)7÷(xy)4;
(4)x2m+2÷xm+2;
(5)(x−y)7÷(x−y)5;
(6)x6÷x2.x.
解 (1)a7÷a4=a7−4=a²;
(2)(−m)10÷(−m)7=(−m)10−7=
(−m)3=−m²;
(3)(xy)7÷(xy)4=(xy)7−4=(xy)3=
x3y3;
(4)x2m+2÷xm+2=x2m+2−m−2=xm;
(5)(x−y)²÷(x−y)5=(x−y)7−5=
(x−y)²;
(6)x6÷x².x=x6−2+1=x5.
总结 应用同底数幂的除法时，必须明
确是底数不变，指数相减，切勿与乘法混淆.
答案：(1)
$a^{7} ÷ a^{4} = a^{7-4} = a^{3}$
(2)
$( - m)^{10} ÷ ( - m)^{7} = ( - m)^{10-7} = ( - m)^{3} = - m^{3}$
(3)
$(xy)^{7} ÷ (xy)^{4} = (xy)^{7-4} = (xy)^{3} = x^{3}y^{3}$
(4)
$x^{2m+2} ÷ x^{m+2} = x^{(2m+2)-(m+2)} = x^{m}$
(5)
$(x - y)^{7} ÷ (x - y)^{5} = (x - y)^{7-5} = (x - y)^{2}$
(6)
$x^{6} ÷ x^{2} · x = x^{6-2} · x = x^{4} · x = x^{4+1} = x^{5}$
答案：$-a^7$
解析：
根据幂的乘方运算法则，有$(−a^2)^5 = (-1)^5 × a^{2 × 5} = -a^{10}$。
根据同底数幂的除法运算法则，有$-a^{10} ÷ a^3 = -a^{10-3} = -a^7$。
