Hey, everyone. So by now, you should have your completed table of all the exponent rules. That whole page should be fully filled out. And in some problems, what you're going to see is you're going to see a generic exponential expression and they won't tell you which rules to use. What I'm going to show you in this video is that in these types of problems, you're usually going to have to use multiple exponent rules combinations of them to fully simplify expressions. And so what I want to do is rather than show you a step-by-step process, it's actually really more of a checklist. You're going to sort of navigate through this checklist in really no particular order just to make sure that you've checked all of these things, and then your expressions fully simplified. Let's just jump into this first problem so I can show you how this works. So we have this first problem, 3x to the negative fifth to the in that whole expression squared, and then we have negative 2x to the fourth, and that whole expression is cubed. One of the first things you want to check for is that you have no powers raised to other powers. So, for example, I see a power on top of a power, in fact, I have a power on top of this whole expression over here, so I can use the power rules. I can basically multiply exponents and distribute them into everything that's inside the parentheses. So let's go ahead and do that first. This 3 goes into the x to the negative fifth and the 3, and so or sorry, this 2, so this becomes 3 squared and then this becomes x to the negative fifth power, squared. And then over here what happens is I have the 3 that distributes to each one of these things, and this becomes negative 2 to the third power, and then I have x to the fourth to the third power. Alright? Now I'm still not done because I still have powers on top of powers, so I have to sort of simplify this again one step further. This just becomes 3 squared, and what happens to the x to the negative fifth, to the second power? You have to multiply the exponents. So this just becomes x to the negative 10, and now you can just drop the parenthesis. Now what happens over here, here I have negative 2 to the third power, then I have a 3 outside of a 4, multiply those exponents, and then this just becomes x to the 12th. So that's what these two expressions became. Alright. So now we have no more powers on top of powers, so we're done with that step. One of the other things you want to check for is that you have no parentheses when that's all left over. Now I only see one parenthesis over here, and that's actually a number. And so we're actually going to use another rule right here, or another thing in this checklist real quick. Make sure that all your numbers with exponents get evaluated. So in other words, the 3 cubed just becomes 9. I have 9x to the 10th, x to the negative 10th times, and this becomes negative 8, over here. I'm actually just going to drop that. Negative 8 x to the 12th. Alright. So here we have all numbers with exponents have been evaluated. Alright. Let's keep going. What are the other things you want to check for is that you have none of the same bases that are multiplied or divided. Here, what I have, I have an x to the negative 10th power. Later on, I have another term that's x to the 12th power. That's not as simplified as it could be because I could really just merge those into one term by using the product and quotient rules. I can either add or subtract the exponent based on whether they're products or quotients. So here's what I'm going to do here. I'm going to do 9, and then I'm just going to flip the order of some of these things. All these things are multiplied, so I can flip the order. This is 9 times negative 8, and then we have times x to the negative 10 and then times x to the 12th. But because I have the same base, I can just add their exponents, so I'll just do that right here. This is going to be negative 10 +12 power. Alright. Now what also happens here is I noticed that I have some numbers that are now multiplied 9 times negative 8. So one of the other things that you can do is just make sure that all your operations have been performed between numbers. 9 times negative 8 can simplify to negative 72. And then what happens here as a result of this product rule is I just get x squared. Alright. So we've done we've done no parentheses, we've done no same bases. The last couple of things you want to check for here is that you have no 0 exponents or negative exponents because then you can just evaluate it to 1 or you can use the negative exponent rule to flip stuff on the bottom or the top depending on where it is and then rewrite it with a positive exponent. Alright? So we've checked for no 0 and no negative exponents. So that means we're done here, and this isas simple as this expression could possibly be. I can't simplify this any further.