What are the fundamental laws of positive integral exponents?

Answer 1

Note that most of the laws for exponents are equally valid for negative, and fractional, exponents. In part, that is because negative and fractional exponents are DEFINED so that those laws continue being valid.Using "^" for power, and "*" for multiplication, some of the fundamental rules are:

a^b * a^c = a^(b+c)

a^b / a^c = a^(b-c)

(a^b)^c = a^(bc)

a^c * b^c = (ab)^c

All of these are valid for any real exponent - including negative and fractional numbers.

Answer 2

ax * ay = a(x+y)ax / ay = a(x-y)

(ax)y = a(x*y)

ax * bx = (ab)x