A lot of students, over the years, keep making the same exponent mistakes. I’m going to go through some of the exponent rules so you don’t make the same mistakes I see kids make over and over again. Let’s get these rules straight once and for all. Let’s go to the board.

### Same coefficient rules

One of the exponents rules students confuse is, if you have X2 x X3, you have the same coefficient here, and you’re just multiplying X2 x X3; students will multiply the exponents. They’ll say X2 x X3 =  X6. That’s wrong. You don’t do that. Let’s get this straight once and for all. It’s X2 x X3. You add the exponents when you multiply two of the same coefficients. X2 x X3 = X2+3; X5. You add the exponents when you multiply exponents with the same bases.

Another exponent rule students confuse is if you take (X3)4. What they often do wrong is they will add these exponents; they’ll just say that’s X7. That’s wrong. Let’s get this straight once and for all. If you have an exponent and you’re raising it to another exponent, that’s when you multiply the exponents. It’s the same as X3×4, or X12, final answer.

Sometimes, students make this mistake: If you have division with exponents. If you have the same base for a numerator and denominator, but it’s X6/ X3. Sometimes, students will say, “I’m just going to divide those exponents.” What they say wrong is they’ll say it’s X6/3 = X2. That is completely wrong, do not do that. What you want to do when you divide exponents, you subtract the exponents from one another. X6/ X3 is the same thing as X6-3; X3, final answer.

One last error I want to show you, that students often make, is if you have(2X)3. What students often do wrong is they will only apply the exponent to the X. They’ll say “That is 2X3, final answer.” That is completely false. Do not do that. What you’re going to do is apply the exponent to each entity in the parentheses. The answer to (2X)3 is the same thing is 23 x X3= 8X3, final answer.

Just go over those 4 rules I taught you, and you shouldn’t make any careless mistakes when you see an exponent problem on the SAT.