When do we add exponents and when so we multiply exponents?

If we have a variable raised to a power times another variable raised to a power, we add the exponents.

For example,  x^2 * x^5 = x^7

If we have a variable raised to a power and that quantity is raised to another power, then we multiply exponents.

For example,  (x^2)^5 = x^10

It's easy to illustrate this.

x^2 * x^5

Think of x^2 as x * x and x^5 as x * x * x * x * x

Notice there are 7 x's total, therefore when multiplying it's x^7.

(x^2)^5

Think of x^2 * x^2 * x^2 * x^2 * x^2

and x^2 = x * x

Therefore we now have x * x * x * x * x * x * x * x * x * x = x^10