Videos

Laws of Exponents

Added Mar 13, 2017 •

Copy this URL:
Embed code:	<iframe class="edlio-embed-player" type="text/html" width="640" height="360" src="//talbert.fvsd.us/apps/embed/?v=140610" frameborder="0" allowfullscreen></iframe> Change dimensions

Show Transcript

hi everybody how we doing today we're going to be talking about the laws of exponents basically what we're talking about is how do exponents work and what do we have to do when we're using them are their guiding principles that we use when we use exponents and yes of course there are so let's start with example problem let's start with x squared times x cubed which is another way of saying x x x x x x what time is X which is another way of saying really just X2 V isn't it what I want you to see here is X to the fifth is shorter version of x squared times x cubed but they're equal to each other because x squared times x cubed really is 5 x as being multiplied together so what can you do Zach squared times x cubed you can make it x to the fifth and you might be noticing something interesting about those numbers well let's look at another example what if you have end of the force x end of the 6th we could write that out and expand it we know end of the 4th is n x n x n what time is that and end the sixth is + x + x + x + x + x n and that basically means we have ended the 10th because AR-10 ends Alba multiplied together there notice that you started with the four and a six and you ended up with the 10 and can you add x squared times x cubed you started with a two and a three and you ended up with a five interesting something happened there what was it here is the law of exponents that applies to this situation if you have x to the something times x to the something else what do you do with the first exponent in the second exponent the law of the laws of exponents tells us that we should add those two exponents together to get us some and then we can shorten up all expression and make it nice and tidy so we added the four in the six to make end of the 10th we added the two in the three to make x to the fifth this is a law of exponents know if you can't remember this law of exponents you're okay because when in doubt just write it all and then you can add it up and you'll get the right answer but the law here gives us a shortcut so that we don't have to write it all out okay so here's another example problem if you have D cubed x p squared times D squared times B to the 4th what we really have here is d x d x d and then later there's another d x d so we have D2 V and then peace Square in their p x p x p - 4th which is p x p e x p x p Tempe okay so we have six peas there and 5DS do you see why we can just summarize this as D2 v p to the 6th I think you can but just in case when doubt write it out when this d x d x d x p x p x d x d x p x p x p x p yes and now hopefully you see why we can just shorten it to did v x Peter the 6th it's the law of exponents what do you do with the exponents you add them up now do we add the five in the six here to make an exponent 11 know because the five stays with Addy's and the six days with the peas hopefully that makes sense too alright let's just try one more what have you have two cubed x q X to let me try that again what have you have two cubed * 2 well isn't that second to really like two to the first Power and in this case wouldn't we add the three plus the one  to get do the force sure but if we're not sure when this p 2 x 2 x 2 x 2 okay that is 2 to the 4th exponents tell us so we can add and that makes these problems really easy so  we could say 2 to the 4th power is 16 or Wii just call it to the 4th power  how about you try a couple what if you needed to do this and simplify it or what if you needed to evaluate this in other words tell me what this comes out too if you multiply it all out when will check our answers tomorrow okay what about a division problem where instead of x to the sixth times squared it's x to the sixth divided by x squared in this case what are we going to do put when in doubt write it out we got six x's on the top we got two x's on the bottom and if you notice here what we can do is just like reducing fractions if you have an is here in an X here can't wait to scratch him and then you've got another X here and another X here can't we scratch those out they cancel each other out right okay good so what we have left we have x x x x x x x that's just x to the fourth over one which is really just x to the fourth isn't it interesting we started with a six and a two and we ended up with a for the law in this case tells us that  we take those Jack's donuts and we subtract we do 6-2 and that gave us our for the laws of exponents tell us in situation that we should subtract the two exponents when it's a division problem like this now again what if you forget the law it's okay when in doubt Susie to the 14th over Z to the 7th should be easy to the Z to the 7th because 14-7 is 7 and that's the law YouTube  14 - equals 7 what if you have a 8 of the 30th over Z to the 12th do we do 30-12 in this situation now play zanzis don't mix so in this situation there's nothing you can do to simplify it you just leave it the way it is all right what if we do have some different very pause but we have some same variables to okay take the ones that are the same and subtract exponents so X cubed on top minus x squared on bottom 3 - 2 is one and XR with the wise you have a two on the top and there's an invisible one on the bottom so 2-1 is one so really there's just x to the first why do the first it's just asked why  should be right it out just to show you why sure X cubed y squared on the top is XXX y y and x squared y on the bottom is xxy and we can just match up and scratch match and scratch match and sky there's a match we scratch them out what's left there's an X and A Y over a one which is really just ask why which is like x to the first why the first and I think you get it by now so simplify this do something with that six in it 3 and then got some asses you got some tees this is going to be S2 the what tea to the what if you can do these problems you're all set and that's all we got for today's so thanks for listening and I will see you tomorrow

Uploaded by Jeff Marbut.

Videos

Laws of Exponents

More videos from Jeff Marbut