in this video we're going to talk about multiplying and dividing monomials and Powers so let's start with the basics what is 4^ 2 * 4 Cub whenever you multiply two monomials with the same base in this case four you are allowed to add the exponents so 2 + 3 is 5 so this is going to be 4 to the 5ifth power so here's another example 3 to the 7th * 3 to 4th all you need to do is add 7 + 4 7 + 4 is 11 so this is 3 to the 11th another example is X2 * X Cub this is going to be X raised 2 + 3 which is 5 now to check it x^2 is x * x x Cub is x * x * X notice that we have five x variables multiply to each other and and that's why it's X 5th here's another example B 6 * B 8 go ahead and try that one so all you got to do is just add 6 + 8 and this will give you 14 so that's what you need to do when you're multiplying monomials with the same base you should add the exponents now what about dividing powers what's 7 to 8 / 7 3r when you're dividing two numbers with the same base you need to subtract the exponents it's 8 minus 3 which is five so this is going to be 7 to the 5th power try this one 2 6 / 2 3r 2 to 6 is what we need to do is subtract six and three which will give us three and 2 to the 3r is 8 so a is the final answer go ahead and work on these two examples so the first one is going to be 7 - 2 which is simply positive 5 the next one is going to be 3 - 7 which is4 now if you have a negative exponent you need to move the X variable from the top to the bottom and then it's going to change sign so this is equivalent to 1 x 4 to confirm it you can do it this way X Cub is simply 3 x variables multiplied to each other whereas x 7 represents 7 x variables multiplied with each other we can cancel three on top and three on the bottom leaving four left over on the bottom so that's why it's 1X 4 here's another example go ahead and multiply 3x^2 by 5x 4 if you ever see a problem like this what we need to do is multiply the constants first 3 * 5 is 15 and then multiply the variables x^2 * x 4 that's going to be x 2 + 4 which is 6 so that's what we need to do when multiplying two monomials together now here's another example multiply 6 x^2 y Cub by 4 x Cub y 5 so let's begin by multiplying 6 * 4 6 * 4 is 24 next let's multiply x^2 by X Cub 2 + 3 is 5 so this is going to be x to the 5th power and then y Cub by y 5th 3 + 5 is 8 and so that's it for that example try this problem what is y Cub * y 6 / y to 4 the first thing we should do is multiply the two uh multiply yq by y 6 on top first so 3 + 6 is 9 now we could divide y 9 by y 4th this is going to be 9 - 4 which is 5 try a similar problem a cub / a 4th * a 5th so first let's multiply these two 4 + 5 is 9 and now let's divide so this is going to be 3 - 9 which is -6 and because we have a negative exponent let's move the a variable from the top to the bottom so the final answer is going to be 1 / a to the positive 6 go ahead and divide these two monomials together 12 x to 4th y 8 / 4X Cub y 4th 12 / 4 is 3 and then we have x 4 - 3 and then y 8 - 4 4 - 3 is 1 8 - 4 is 4 so we can write it as 3x y 4 all right let's try this one 35 x to the 7th y to the 9th and let's divid by 63 x to 4th y 5th 35 is 5 * 7 63 is 9 * 7 and then we have x 7 - 4 and Y 9 - 5 which initially Will Go On Top now we can cancel the sevens 7 - 4 is 3 9 - 5 is four and we have a nine on the bottom so this is going to be the final answer for that problem consider these three problems what is 2 to 3r * 2 7th and then 2 5 * 4 5th and also 2 5 * 4^ 2 or rather 4 Cub now in the first example notice that we have the same base if you have the same base all you need to do is simply add the exponents so it's going to be 3 + 7 which is 10 so the answer is 2 the 10th now in the second example example notice that the the base is not the same but the exponents are the same when the exponents are the same you can multiply the bases 2 * 4 is 8 so this is going to be 8 to 5th in the last example we don't have the same base or the same exponent so we need to change it one way or the other so what we could do is get the same base first for example 4 is equivalent to 2^2 and when you raise 1 exponent to another you need to multiply 2^ 2 rais to the 3 power is going to be 2 6 because 2 * 3 if you multiply these two it will give you six and then you can add 5 + 6 which is 11 now if you type that in your calculator 2 to the 11th power is 248 so that's the final answer but now let's do it another way another way in which you can do it is you can convert it to the same exponent 2 to the 5th power is 32 or 32 to the 1st power 4 to the 3 is 64 to the 4 power so if you multiply 32 by 64 you're going to get 2048 to the first power so as you can see whenever you have the same exponent you can simply multiply the basis and if you have the same base you can add the exponents now I want to show you one of my algebra courses that might be useful to you if you ever need it so go to udemy.com now in a search box just type in algebra and it should come up so it's the one of the image with the black background so if you select that option and if you decide to go to course content you can see what's in this particular course so the first section basic arithmetic for those of you who want to focus on addition subtraction multiplication and division and it has a video quiz at the end it's a multiple choice video quiz you can pause it work on the problems and see the solutions it covers long division multiplying two large numbers and things like that the next tutorial is on fractions adding subtracting fractions multiplying dividing fractions converting fractions into decimals and so forth so you can also take a look at that next solve the linear equations which we covered and just more examples if you need more help with that the next topic order of operations which is also useful uh graph in linear equations you need to know how to calculate the slope needs to be familiar with the slope intercept form standard form and just how to tell if lines are parallel perpendicular and so forth and there a quiz that goes with that as well the next topic is on inequalities and absolute value Expressions which are also see in a typical algebra course and then we have polinomial and that's a a long section and then factoring you just that's another topic you need to master and then system of equations you can solve it by elimination substitution there's also word problems as well sometimes you got to solve equations with three variables X Y and Z so that could be helpful next quadratic equations how to use a quadratic formula how to graph them how to convert between standard and vertex form and then you have rational expressions and radical expressions solving radical equations simplifying it things like that and every section has a quiz so you can always review what you've learned if you have a test the next day so here we have complex imagin numbers you need to know how to simplify those exponential functions logs I have a lot of videos on logs and then this is just functions in general vertical line tests horizontal l test how to tell what functions even or odd and then conic sections graphing circles hyperbolas ellipses parabas and things like that there's two video quizzes because it's actually a long section and finally arithmetic and geometric sequences and Series so that's my algebra course if you want to take a look at it and uh let me know what you think for