计算[(n-m)^3]^p.[(m-n)(m-n)^p]^5注：^3是3次幂P为偶数时得（m-n)^8p+5P为奇数时得（n-m)^8p+5

Question

计算 [(n-m)^3]^p.[(m-n)(m-n)^p]^5
注：^3 是3次幂
P为偶数时 得（m-n)^8p+5
P为奇数时 得 （n-m)^8p+5

Answer 1

P为偶数时:
[(n-m)^3]^p.[(m-n)(m-n)^p]^5
=(n-m)^(3p)*(m-n)^5*(m-n)^(5p)
=(n-m)^(3p)*(m-n)^(5p+5)
=(m-n)^(3p)*(m-n)^(5p+5)
=(m-n)^(8p+5)
因为P为偶数时3p也是偶数.
P为奇数时:
[(n-m)^3]^p.[(m-n)(m-n)^p]^5
=(n-m)^(3p)*(m-n)^5*(m-n)^(5p)
=(n-m)^(3p)*(m-n)^(5p+5)
=(n-m)^(3p)*(n-m)^(5p+5)
=(n-m)^(8p+5)
因为P为奇数时(5p+5)是偶数.