利用等式1+2+3+……+100=5050,化简:(x^100y)(x^99y^2)(x^98y^3)……(x^2y^99)(xy^100)

x^100y)(x^99y^2)(x^98y^3)……(x^2y^99)(xy^100)
=x^(100+99+...+2+1)y^(1+2+...+99+100)
=x^5050y^5050
=(xy)^5050

(x^100y)(x^99y^2)(x^98y^3)……(x^2y^99)(xy^100)
=x^(100+99+...+2+1)y^(1+2+...+99+100)
=x^5050y^5050
(xy)^5050

(x^100y)(x^99y^2)(x^98y^3)……(x^2y^99)(xy^100)
=x^(1+2+3+……+100)*y^(1+2+3+……+100)
=x^5050*y^5050

用乘法交换律把相同的写在一起再用幂的乘法原则

x5050y5050