 In series two, we introduced exponents and radicals. So let's take a look at how exponents and radicals, how we can incorporate that with the equal sign, right? Let's say we have something starting off really simple. Let's say we have x squared is equal to eight. Now, again, we want to get, if they say solve for this, the question would be solve, simple thing to say. Sol for the square. So to get rid of the squared, we have to take the square root of it, right? So what you end up doing, if you want to get x by itself, let's take the square root of one side and you got to take the square root of this, right? Now, squared of x squared, again, this is series two, we should not say equal x plus, square root of x minus two equals one. So this becomes x is equal to square root of eight. If you're going to reduce this to its lowest terms, you have to break it up into its prime truth, right? So if you're like, we do this square root of x plus its prime, so this becomes two, square root of, okay? So for this one, the answer is just going to be x is equal to two square root of two. Now, I'm not going to continue to go over this stuff, okay? How you reduce radicals and, you know, exponents, if you put a, and how you put a, you know, the number here goes into the denominator. Again, if you haven't seen the stuff, and this stuff just usually is one of the main stoppers, main things to stop people from progressing on in mathematics. So if you don't know this, seriously go back in series two and look at that stuff and do a lot of examples, because this is, you know, the next step up from addition to subtraction and multiplication division, okay? So again, if you have x squared, you want to isolate the x, you take the square root on both sides, you got to take, you know, square root of eight becomes two square root of two. So x is equal to two, x is equal to two square root of two. Let's go take a look at, you know, a little bit more complicated stuff and add a radical in there as well, okay? So we did x squared is equal to eight. We solved for that. We found out that was two square root of two. Let's do a radical, you know, a single radical and see what we do to isolate the variable if we have a radical or something, okay? The root of something. So let's say you had, let's say you had the cube root of three is equal to, cube root of x is equal to three. And again, you want to get the x by itself, right? Now the simplest way to do this, if you're dealing with radicals, is to change them to powers, okay? To change them to an exponent. So an exponent, you grab the three, bring it to the denominator of the power. So this just becomes x to the power of one third is equal to three, right? Now you haven't done anything to this. You haven't reduced anything. All you've done is rewrite the radical as a power. Now the way you get rid of this, what you need to do is do the opposite in the power, right? Now that's one over three. And if you want to do the opposite of one over three to get rid of one over three, you multiply it by three over one. So what you can do in the power, take this to another power. And that's another way of saying how you get rid of exponents and radicals. You're just dealing with exponents and you're doing the flip of it, the inverse of it in the power. So that's one over three. You take this to the power of three over one, right? So you've got to take this to the power of three over one. One third times three over one. The three in the top kills the three in the bottom. So this just becomes x, comes x, right? And three to the power of three over one is just three cubed. Three cubed is going to be 27. And that's the final answer for this one. Now we're going to do a little bit more complicated problems with this and start introducing both addition and subtraction into the equation and multiplication and division. So what we're going to end up doing is working our way into harder and harder and larger and larger problems. And in the end, we'll end up doing what gigantic, ugly problem. Solving for the x to find out what it means. So let's do a combination of these expressions that we've dealt with and see how we can reduce, start reducing things. Reducing or solving larger expressions. Or larger problems, solving larger problems. Solving larger problems.