 This video is called Multiplying Polynomials 2. There are three different problems in this video. Make sure you watch the video and see all three problems and take notes for all three problems as they're all just a little bit different and we want you to know how to do all three kinds. This first problem, we have a term, negative 6xy to the sixth. It's in parentheses and it's raised to the power of 2. So basically what this is saying is to take what's in the parentheses, the term negative 6xy to the sixth and multiply it by itself. So now we have two polynomials. There's nothing in between the two parentheses so I know it's multiplication. So just like what we've been working on, a negative 6 times a negative 6 is a positive 36 and then we will add our exponents. The x's, remember if there's nothing there it's really an exponent of 1 so x to the first times x to the first you'll add those exponents and get x squared. y to the sixth times y to the sixth you'll add those exponents and get y to the twelfth. So you end up with 36x squared y squared. Now let's look at the second example. This time we have a term 6x to the fourth g squared that's in parentheses and it's raised to the power of 5. So technically we might have to write 6x to the fourth g squared 5 times but I don't really want to do that because it takes a lot of room, there's a lot of paper, it takes a lot of time so we're going to work on a shortcut where when you have a term raised to the power it's called power to a power and we can do some multiplication and some shortcuts. Please remember this 6 really has an exponent of 1. So what we're allowed to do it's kind of like a distributive property where this 5, the exponent on the outside is going to multiply with every exponent on the inside. So we really have 6 to the 1 times 5 x to the 4 times 5 and g to the 2 times 5. Now this time we don't add the exponents we multiply them because when we have a power an exponent raised to another power another exponent you actually multiply the exponents together so we'll get 6 to the 5th excuse me x to the 20th and g to the 10th the one thing I would do then to make this even better is 6 to the 5th is 7,776 x to the 20th g to the 10th One more and this is going to combine a power to a power and then combining like terms as well there's a lot going on in this problem we have my first term the negative 2x to the 3rd y to the 4th all raised to an exponent of 2 so that 2 is going to have to distribute with the 2, the x and the y and then in my second term the 3x to the 5th raised to the 4th that exponent of 4 is going to have to attach or multiply or distribute with everything in the second set of parentheses so let's see what I get when I distribute or do the power to the power with the 2 so negative 2 is really negative 2 to the 1st so I'm going to have to do the 1 times 2 x to the 3rd raised to the 2nd will be x to the 3 times 2 and y to the 4 times 2 so I end up with negative 2 squared x to the 6th y to the 8th and now let's go ahead and do my second term what I've been outlining in green the power to the power this time the exponent is a 4 so I will do 3 to the 4th and x to the 5 times 4 so I have 3 to the 4th x to the 20th now I have to combine all the like terms that I have in one big multiplication problem like this let's see I've got negative 2 squared which is a negative 4 x to the 6th y to the 8th 3 to the 4th let's clean that up a little bit 3 to the 4th is 81 and x to the 20th well the like terms I have would be the negative 4 and the 81 which gives me a negative 324 and then let's see I have an x to the 6th and a y to the 20th so that will be x to the 26th and then the y to the 8th is left over by itself so it started as a power to a power where I multiplied my exponents together and then when it came time it was just one big multiplication problem and I wanted to combine some like terms with these x's it's not a power to a power anymore so you would add the exponents and get 6 plus 20 which is 26 so be careful when you have an exponent raised to an exponent that's when the exponents multiply but when you're just combining like terms and multiplying down here the 6th and 20 you end up adding