x^3 is a product of three factors of x: x * x * x.
x^7 is a product of seven factors of x: x * x * x * x * x * x
When you multiply x^3 by x^7, you end up with a product of 10 factors of x:
x * x * x * x * x * x * x * x * x * x
A product of ten factors of x is x^10.