Algebra II Basic 5.1
Mar 31, 2021
Chapter 5.1 of the Basic Algebra II
Algebra two basic. Monomials and scientific notation. As we get started, there are some rules that we need to look at, dealing with exponents. We have the base a to the power of M multiplied times the base a to the power of N this equals the base a, with the exponents M and N, added together. Our next rule, the base a to the power of M, multiplied times the power of N this equals the base a, with the power of M N this is known as the power to power rule, where the exponents are multiplied together. The next rule, the base a and B, both multiplied by the power of M equals the base a to the power of M and the base B to the power of M here different bases have the power distributed to each one of them.
The next exponent rule is the base a to the power of zero. This equals one. In the last row we're going to look at is the base a to the power of M over the base a to the power of N this equals the base a with the powers M subtracted. N here we have the same base in fraction, which is being divided, and the exponents are being subtracted. Now we're going to take a look at some examples. Our first example, a to the power of two, and four a to the power of four. Our base is a this is the first rule where we said power and power are added, so two plus four is 6. In our next example, our power is excuse me or base is X this is the power two power rule, so we have four times three. Four times three is 12. Looking at example three we have a power on the outside. This power is affecting everything inside the parentheses. Individually, we'll take a look at that. That start at the beginning, going from left to right. We have three negative three to the power of three.
Negative three to the power of three is positive 27. It's the same as negative three times negative three times negative three. Our base C is next. This is like our second example where we have power to power, so if we're looking at power to power, we are multiplying. Power to power is power times power, two times three is 6. Our next base is D again power to power, power times power. And that is, three times 5 is 15. Example four takes two monomials and is multiplying them together, and we start at the beginning of each one, and work our way across matching the pieces, so we match number times number. Negative two times negative 5 is positive ten. Our base is a, and we have an a in each one of these parts. You'll notice that this one does not have an exponent, so we could slide a little one in there, kind of as a placeholder for us, to remind us that there is one a, because our base is a, and now we're looking at the example one.
Where we are taking the powers, and we're adding them with like bases. So three plus one is four. Our next base is B and this one does not have any power to its brutal slide a one in there again as a reminder. And again, this follows the rule like we did in number one. And that is, adding the powers of one plus four is 5. Looking at example 5 we have three times X to the zero power. We think back to that rule of anything with a zero power is one, we do have a three in the front, so we want to hold that there. And X to the zero power is one. Let's put parentheses around it to keep it separated, so it doesn't look like the number 31, and we could see that three terms one. It's going to be three. Here are a couple fraction examples as we wind up our examples for today. And to do a fraction example, it's always good to write a fraction line. In this particular problem it wants us to locate the base that has the largest exponent.
If I look at that I can see that X to the 7 is larger than X to the third, and I'm going to take the base X and I'm going to write it on the line right across from where it is. Now if we follow that rule, it says we take one power and we subtract the other, and we always want this to be a positive number, so we're going to take 7, and we're going to subtract three. Now, you can put a number one down under here, because there is nothing left down here. Or you can simply write it as X to the 7th power. In this particular fraction, again, we're going to start with the fraction line, we're going to locate the base that has the larger power, so a 5th compared to 8 of the tenth a to the tenth is larger. It's on the bottom, so I'm going to put my base on the bottom. Then I'm going to subtract my powers again, the one that I used minus the one that I didn't use. So ten -5 is 5.
Now, in this situation, we can't leave this an empty blank. We do have to put something there, and a good placeholder is the number one, because it doesn't change the value of that particular fraction, and it shows us that it is a fraction in not whole number. You are not able to take this one and eliminate the one like we did an example 6, because this remains a fraction, where this one did not. And those are the examples for today. Look at for your homework assignment, in classroom, or on the website, and I will talk to you next time.