如何证明指数定律
如何证明指数定律
a的m次方乘以a的n次方等于a的（m+n）?
a^n = a*a*.*a (n个a)a^m = a*a*.*a(m个a)a^n * a^m=a*a*.*a * a*a*.*a(n个a)(m个a)= a*a*.*a(m + n)个...
谢谢，请证明
(a*b)^m=a^m * b^m;
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(a^m)^n=a^(m*n);
.....
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(a*b)^m = (a*b) * (a*b) *.........* (a*b) （m个(a*b)）---所以有m个a和m个b
= (a * a * ......*a) * (b * b * ........ * b)
(m个a) (m个b)
= a^m * b^m
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(a^m)^n = a^m * a^m * ............. * a^m
(n个 a^m)
= (a * a *............* a) * (a * a *............* a) *...........*(a * a *............* a)
(m个a) (m个a) .......... (m个a)
(m个a)的数目是n ------ a的数目是mn个
= a^ (m*n)