I want to start out saying these last two semesters have been eye opening for me, and I have been so fortunate that many of these students have been making me work in these lessons I've been teaching, as my initial worry is that my lectures would be boring because many of the lessons I've taught seemed really easy, that the first time with an Algebra 1 class I actually entertained the thought that the teacher told the students to ask me a lot of questions to make me really do some explaining. Of course, I know that didn't actually happen. An issue I've been dealing with in both semesters is the students no matter how gifted they are in math have been dealing with misconceptions, and needed to be reminded of exponential rules such as x^m*x^n=x^m+n. Also, another issue is frequently students seem to confuse multiplication with exponents. Yesterday, a group of students when on a practice problem where the answer was 3 to the 10th power immediately said the answer was 30, not realizing that it isn't the same as 3 times 10. Is this a common problem that people have noticed in math? Mostly, what I've been saying to students is correcting them asking them how they came up with that answer, and asking a question such as, "Is 3 to the 10th the same as 3 times 10?" Usually it doesn't take anymore than just asking this, then they usually end up doing something such as smacking themselves in the head and fixing it. Is there a trick or anything that usually gets them to stop doing this, or do they just end up getting it in time with more practice? Also, I thought exponents in 8th grade were a review topic in Common Core based on what they previously learned. Do they do any conceptual lessons in earlier grades to get them to learn the basics and dynamics of exponents that upper grades teachers can refer back to and clear up misconceptions?