Exploring All Four
When in a equation you're multiplying and you have similar bases this is when you would add your exponents. Say you have J^4 times J^6, you would keep the base and add the exponents to get the product J^10. Or say you have 5^2 times 5^7 you would keep the base the same and add the exponents to get 5^9, or 1,953,125.
The time to multiply exponents is when we have parenthesis and an exponent on the outside. Say we have (H^6*X^2)^2 we would distribute the 2 on the outside by multiplying it to each exponent on the inside. So the exponent 6 would become 12 and the exponent 2 on the inside would become 4. And because we have no like terms our final answer would be H^12 times X^4. For a more visual example here's a link, https://www.youtube.com/watch?v=sbfjHOeBOC4.
When you have a negative exponent, for example X^-2 you must put the numerator pair in the denominator to have 1/x^2, the one left on the top. In other word put it into a fraction or move its place. So if you say you have 1/X^-4 move the denominator part to the numerator making it positive X^4.
If you're dividing bases with exponents this is when you have to subtract the exponents. To give an example, say you are given X^2/X^1. Because you have the same base you can proceed to subtract, remember ONLY subtract the exponents if the bases connected are the same. 2 minus 1 is 1 is one so our answer is X^1 or X.