Brian S. answered • 05/22/16
Tutor
New to Wyzant
Prospective Teacher and Tutor
1) I'm assuming that says x times x times x times x. When you multiply two of the same variable, so in this case X, you just need to add their exponents together. So if it's just plain X, then that means its really X1 so the answer is 1+1+1+1 = 4, so X4
2) I can only assume you mean 3x2 times 2xy. Well just go step by step. First you multiply the numbers together, you have a 3 and a 2. 3x2 = 6. Next you have an x2 and an x. Like I said in the first problem you just need to add the exponents together for this so the answer is 2+1 = 3, so x3. And then there's only a y on one side of the multiplication so you just need to add that at the end. So you end up with 6x3y
3) So looks like you're writing (15x2y4) divided by (2x3y2). Alright so we solve this very similarly to the previous problem except instead of multiplication and addition, it will be division and subtraction. First look at the numbers. 15÷2. This would result in a decimal and normally in math we try not to have decimals in our expressions, but maybe you're class is different. If you think it's appropriate to make it a decimal feel free but I am going to leave it as a fraction. So right now I have 15/2. Next let's divide the x's. we have x2÷x3. When you divide two of the same variable, instead of adding their exponents you subtract. so 2-3 = -1. So our new x is x-1. And then do the same thing for y. y4 ÷ y2 = y2 because 4 - 2 = 2. So our answer is (15/2)x-1y2. Not sure how advanced your class is but this can also be written as (15y2)/(2x) because x-1 is the same thing as 1/x.
4) So this is an easy one. A trick I used to use when I was learning this is to assign shapes to every different variable. So circle all of the numbers that are x and box all the numbers that are y. Also make sure to include the sign of the number directly to the left of it. So now just combine all the ones you circled, and combine whatever was boxed. In this case we combine 2x, 4x, and 12x to get 18x. And for the ones we boxed we only have -6y. So our new answer should be 18x-6y.
5) For this we are going to do the same thing we did in question 4. Except this time we need to consider two things. First, understand that x, y, and xy are 3 different variables and that none of them can be added together. Second, when you see in a problem, 2 + (-20), you need to distribute the sign. It's easier to look at it this way, picture that it's 2 + 1times(-20). What is 1 times -20? It's -20, so now we have 2 - 20. We will do the same thing for question 5, so we have 14x + 2xy + (-20x), we will turn this into 14x + 2xy - 20x. Now we combine the same terms, so we combine 14x and -20x to get 14x-20x = -6x. There are no terms to combine with 2xy, so now we have 2xy-6x as our answer.
