How would you explain how the laws of exponents work with rational exponents?
They work the same with any exponents: rational or irrational, and even imaginary and complex.
x^a * x^b = x^(a+b)
(x^a)^b = x^(ab) etc.
x^a * x^b = x^(a+b)
(x^a)^b = x^(ab) etc.