Question

What is a general rule for simplifying expressions like x^a .x^b? where does this rule

comes from

Answer 1

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)