You add exponents only when two numbers have the same constant, but the exponent does not have to be the same. And you can only add exponents when you are multiplying them. So,
4 to the 5th power x 4 to the 7th power would require you to add the exponents and keep the constant (which is 4). See, 4 is common constant so you are allowed to add exponents. If it were this: 4^5 x 5^4, you cannot add exponents.
You multiply exponents when you have a number with an power to the power, like:
(5^6)^5, which means you will multiply the exponents, and you will get 5^30.
Hope this helps