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Funky Exponents

Added Mar 17, 2017 •

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hi everybody today we're going to talk about funky exponents to get a little bit weird what happens when exponents don't quite Act I'm already talked about this kind of problem if you have x to the 6th / x squared you just do 6-2 and you get x to the fourth but the situation got flipped upside down what if you had x squared on top and next to the sixth on the bottom what if the top exponent is small then the bottom exponent what are we doing this situation will the rule the law of exponents says that we're supposed to subtract so we're supposed to do top next moment - bottom exponent so it's supposed to be 2-6 it's just that comes out to -4 that's kind of strange can you even have if a negative exponent are we allowed to do that well the answer is yes you are allowed to have a negative exponent but we need to understand what that means so understand what that negative exponent means we're going to write this out so  x squared is x times x to the 6 power x x x x x x x x x x x and we know that we can match these things up and scratch them out so we're going to scratch those and scratch those and so what you see here is if we win and outright it out we would really have one on top as a placeholder and then x x x x x x x x on the bottom to the fourth on the bottom so what I want you to see here is that that thing that came out to x to the negative 4th could also be written as 1 over X the 4th  and they're equal so the rule of negative exponents is that you are allowed to have negative exponent it just means that whatever that power is it's happening in the denominator Okay negative exponents mean powers in denial here's what I mean if you have eight to the negative 2 that means that we're still going to square the 8th we're still going to do 8 x 8 and get 60 for but that 64 is going to happen where it's going to happen in the denominator so it's really not 64 and it's not negative 64 it's one over 64 let me give you another example 10 to the negative 3 power is still going to be 10 x 10 x 10 but it's going to be one over 10 x 10 x 10 okay how about a couple more examples just to really make sure we got this if you have any number to the negative 4 power it means you're going to do that number times itself times itself times itself but it's going to happen in the denominator so it will be one over that number the 4th power and if I did 5 to the negative 2 power it means I'm going to square the five I'm going to do 5 x 5 but where am I doing 5 x 5 I'm doing it in the denominator of a fraction so it's not going to be 25 and it's not going to be -25 it's going to be one over 25 when I have five to the night power notice the answers and negative the negative exponent doesn't mean a negative answer the negative exponent means to the power is in the denominator of a fraction what's the negative exponent doesn't mean the answer's going to come out negative it means that the thing that's getting squared is getting squared in the denominator of a fraction all right so let's see if you got that in your journals I want you to evaluate what is 7 to the negative 2 power what would that come out to all right now we got another funky kind of an exponent situation what if we had x to the 12 / x to the 12th the rule exponents says you're supposed to do the top exponent minus the bottom exponent will that would be  12 - 12 which comes out to zero again that's a strange funky exponent there because are you allowed to have something to the zero with power well I guess you are allowed to have that because that's what this is supposed to come out to  oh wait let me just point out here that wouldn't x to the 12th divided by itself come out to one isn't anything divided by itself equal to 1 so I guess what I'm trying to say here is that x to the zero power equals 1 or  anything to the hero power always equals one because of this rule of exponents so if I asked you what is 8 to the 0 power did tell me that the answer is one because anything to the power of 0 is 1 what's 11 to the 0 power 1 what's 2 point need to the zero power one what's 119 to the 0 power 1 what's one of the 0 power one anything to the power of 0 turns out to one which makes this last practice problem really easy and once you've got that you've got the whole scoop on funky exponents so  see you next time

Uploaded by Jeff Marbut.

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Funky Exponents

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