So, x^a*x^b would simplify to x^(a+b)
As for the proof of this,
Given that addition, subtraction, multiplication, and division are already known and don’t need to be proved, we know:
x^a = x*x*x… (a times)
x^b = x*x*x… (b times)
If we were to multiply these two expressions together, we’d simply get:
x^a*x^b = x*x*x… (a+b times)
And thus, that is why
x^a*x^b = x^(a+b)
