### Video instructions and help with filling out and completing How Form 2220 Index

**Instructions and Help about How Form 2220 Index**

In this video we're going to focus on simplifying exponents but let's go over some basic properties what is X to the fourth x x to the fifth what is that equal to whenever you multiply by a common base you need to add the exponents 4 plus 5 is 9 X to the fourth is basically multiplying 4 X variables together and X to the fifth is equivalent to multiplying five X variables together so in total you're multiplying 9 X variables together and so that's why it's equal to X to the ninth now what about division let's say if you divide by a common base what should you do with the exponents you need to subtract X it is 7 divided by X to the 3 it needs to subtract 7 by 3 and that's going to be exit for X to the 7 is equivalent to 7 X variables multiplied to each other and X cubed is simply x times X times X so we can cancel 3 X variables which we'll leave behind for X variables on top and so that's the answer there's another one what is X to the third raised to the fourth power what should we do whenever we raise one exponent to another in a situation like this you need to multiply it's going to be 3 times 4 which is 12 so X to the third raised to the fourth power means that you're multiplying 4 x cubed values and each x cubed is basically three X variables multiplied to each other so if you count all the X variables what we have is a total of 12 and so that's why it's equal to X to the 12 now what about X raised to the 0 power what is that equal to anything raised to the 0 power is 1 so 4 to 0 is 1 now what about X raised to the negative 3 what should we do if we have negative exponents if you have a negative exponent all you could do is take the variable move it to the bottom when you do that the negative 3 will become positive 3 and so it's 1 over X cubed likewise let's say if you have 1 divided by X raised to the negative 4 you can move the X variable to the top any exponent will change sign so it's going to be X to the positive 4 over 1 or simply X raised to the 4th power that is the question theme what is the value of negative 3 squared what do you think that's equal to now what about negative 3 squared within a parenthesis negative 3 squared is basically negative 3 times negative 3 we have two of them so this is equal to positive 9 now what we have here is one negative and two threes this 2 does not apply to the negative sign so we only have one negative sign so this is negative and then 3 times 3 is 9 so the whole answer is negative 9 so just keep in mind the difference between the two you can confirm this in a calculator if you type in negative 3 squared just the way you see it like this you should get negative 9 so tree typing like this in your calculator it should give you positive 9 go ahead and simplify these problems simplify the following expressions so let's say this is the first one here's the next one X cubed raised to the negative 5 and also X to the seventh power divided by X to the 12 go ahead and work on these examples so when multiplying by when multiplying haben bases in to add the exponents 4 plus negative 9 is negative 5 and X raised to the negative 5 is equivalent to 1 over X to the 5th so if you get any negative exponents make it positive now here we have one exponent raised to another so we need to multiply 3 times negative 5 is negative 15 x to the negative 15 is 1 over X to the positive 15 so this is the final answer for that problem now for the last one we need to subtract we're going to take the top number and subtracted by the bottom number 7 minus 12 is negative 5 and this is the same as 1 over X to the 5 now let's talk about that example X is 7th means that we have 7x variables X to the 12 means that we have a total of 12 X variables multiplied to each other so we can cancel all 7 X variables on top and seven on the bottom and notice that we have five X variables left on the bottom and that's why it's run over X to the 5 what is the value of 3x squared raised to the third power go ahead and simplify this expression so 3 is the same as 3 to the first whenever you raise one exponent to another you need to multiply but we have 2 X 1 is here so we need to distribute the 3 to the 1 and to the 2 so 3 times 1 is 3 and 2 times 3 is 6 so this is 3 to the 3rd times X to the 6 so let's drink to the 3rd 3 to the 3rd is 3 times 3 times 3 3 times 3 is 9 and 9 times 3 is 27 so the final answer is 27 times x-rays to six power try this one negative two okay that doesn't look like a - let's do that again negative two X cubed Y to the fourth raised to the second power feel free to pause the video and work on that example so this is raised to the first power and if we multiply by two we're going to have negative.