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[00:00:16]Okay, let me set this point so that I'm explaining everyone can be able to see. Okay.

[00:00:42]All right. All right. All right. All right. All right. All right. All right.

[00:00:46]All right.

[00:00:49]I just want to check with you and please can someone text me on WhatsApp? I just want to check if something this case.

[00:01:16]Let me check if maybe I write. Um, let me use this pen.

[00:01:27]Uh 3x² + 2x - So today we are looking at the exponents. Okay, we want to deal with the exponents.

[00:01:58]So I believe that uh you will listen to me and follow all the steps.

[00:02:08]Okay.

[00:02:10]So right now we'll be looking at the laws of exponents.

[00:02:16]I do have the test book with me so that whenever I'm explaining you guys can understand.

[00:02:27]So let me check the page uh we can use today.

[00:02:33]I'm checking the page that we can use.

[00:02:35]Right.

[00:02:36]The page we can use. I'll try to I'll try not to be fast so that everyone can understand because sometimes no I'm moving in a paraffin speed so then they do complain to say that no no no say please do it slowly but surely why not why not I'm just trying to check the page here so that we can start with The business of the day, guys.

[00:03:11]>> All right.

[00:03:13]All right. It's page 30.

[00:03:19]It's basically page 32.

[00:03:23]Page 32.

[00:03:29]Okay.

[00:03:31]We are looking at the laws of exponents.

[00:03:35]Laws Laws of exponents.

[00:03:41]Exponents.

[00:03:43]Okay. Want to deal with the laws of exponents. So please guys, the laws of exponents.

[00:03:53]So guys, the laws of exponents.

[00:03:59]Basically, we'll be talking about the base exponent.

[00:04:08]or a power. Okay, so in this case power and exponent we're talking about same thing. Okay, we do have a square.

[00:04:19]We do have a square and a cube. So this is grade eight work. So in this case people um in this case the base under the laws of exponents the base we are talking about the number being multiplied. So this is the number being multiplied.

[00:04:52]A number being multiplied as a base.

[00:04:54]Okay. But the exponent of power, exponent of power, we're talking about how many times a base is used.

[00:05:11]Okay, so this is the the the the exponent. Okay, we're talking about how many times a base is used. But with a square we are talking about a number a number raised to power two it's a square but a cube in this case we're talking about a number raised to power what to power three so these are the some of the things that I will be uh talking about okay so I have already outlined the base exponent square and the cube. So first law of the exponent is what is the multiplying power with the same base. Let me write it down here. Multiplying multiplying powers with same base. Okay, we are about to multiply power with what? With same base. So in this case to multiply powers with the same base. If when we multiply the same base when we multiply the same base we add the okay. So a ^ m* a ^ n this will be equals to base m + n. All right. So these are the some of the things that we have to talk about. So I have to make sure that I remind you about all these so that when we move to the to the examples uh whereby we will be simplifying you'll know what to do. Okay. So a exponent m a exponent n² base which is what base exponent m + n right an example in this case an example it can be example two 2 3 * 2 ^ 1 okay 2 ^ Okay.

[00:07:42]3 + 1. 3 + 1 is 4. All right. So, you just have to use a calculator for two exponent four and then you write down the answer. Okay? 2 exponent four and then you write the what the answer.

[00:07:59]So 2 exponent 4 we getting what? We get 16. So the answer here is what? It's 16.

[00:08:05]Right? Let's move to number two. Because here we're multiplying the same base.

[00:08:09]Let's move to number two. Number two we are talking about what? Dividing.

[00:08:16]Dividing powers with the same base.

[00:08:24]Dividing powers with the same base. So in this case when we divide powers with the same base this is what you are going to uh uh to come across a exponent mide by a exponent n. So in this case this we are going to do what? When we divide the powers with the same base, it means we're going to choose one and then you write what you write m - n singular exponent meaning to the exponent m / a to the exponent n.

[00:09:28]money.

[00:09:32]So sometimes eg example when we divide the same base we subtract the exponents. So this is 3 minus 3. Okay. So Divide we are dividing the same base right. So 3 / 3 exponentus same base right exponent what 2 + 3 which is 3 exponent what? 3 exponent 5. So exponent 5. So this equals to 243.

[00:10:46]Okay.

[00:10:50]Let's move to number two.

[00:10:53]Number two. Oh number three. Number three, we are saying this will be the power of a power.

[00:11:05]The power of a power. The power of a power to the exponent.

[00:11:21]This is the power of a. All right. So power multip which will give us what? base MN meaning that two exponent two inside the bracket to the power 2* 2 it's four. So base exponent forces exponent 16.

[00:12:27]Sometimes variable Xon two and then two exponent one. So it will be 3* 1 this exponent one okay right so it's 3 * 1 so it will be what it will be 2 exponent 3 and x this will be 2 * 3 which is 6 2 exponent 3 8. So this will be 8 x exponent 6.

[00:13:42]So every time power of a power do not forget this. Okay. Grade eight. Please please please let's move to number four which is a zero exponent.

[00:14:03]Zero exponent with the zero exponent exponent zero.

[00:14:17]Any number to the exponent zero or any number to the power of zero or any variable to the power of zero one eg it doesn't matter the number it can be 1 million exponent 0 okay it can be 9,000 exponent 0 7 exponent 0 to 1 any number 2x inside the bracket exponent zero it is equals to one. Do not forget this.

[00:14:52]Okay, it's very much important. Do not forget this.

[00:14:57]But 2 + x exponent 0 2 exponent 0 and x exponent 0 just like that in this case. Okay. So let's move to number four. Let's move to number four.

[00:15:31]We are moving to number four now. Number four.

[00:15:36]Oh, it's number five because this was number four. number five is zero exponent any number to the power of 0 is one. Okay. So in this case now negative negative exponent a negative exponent exponent the power always You could divide by one exponent positive.

[00:16:31]Okay.

[00:16:39]Two to the power x 2 to the powerx.

[00:16:49]always the power x 2 -2 always expon So this will be equals to 1 / 4.

[00:17:32]Yes. So let's move to the to the examples. Let's move to the examples.

[00:17:40]Okay. Let's take it now that saying simplify simplify simplify x² * y cubed / x to the power of 3 and y to the power of 5.

[00:18:08]In this case we need to simplify this.

[00:18:12]Okay.

[00:18:18]Right. So divide the same base. Okay. So x exponent 2 - 3 * y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y y exponent 3 - 5 step number x 3 - 2.

[00:18:58]This is wrong. Totally wrong. Okay.

[00:19:10]So 2 - 3 is -1. So it's x1 * y what? -2 1 / x exponent 1.

[00:19:33]Okay.

[00:19:35]multiply by 1 / by y exponent 2.

[00:19:44]Therefore 1 * 1 is 1 / x * y^ 2 it's what? It's x y^ 2. We are done for one example. It was example number one. Example number two.

[00:20:04]Example number two.

[00:20:08]Example number two. We are given um 2 x² inside the bracket 3 multiply by xy.

[00:20:24]Okay. Multiply by xy divide by divide by what? divided by 4 x exponent 3 y - 2 they're saying we need to simplify this look simplify if applying laws all those laws okay we can use uh the multip the multiplying of power with the same base or dividing powers with the same base or power of power or it can be zero exponent negative exponent. Okay. So in this case let's deal with the first one.

[00:21:09]This the power of a power 1 1 * 3 is 3 x x 2 so 2 * 3 is 1 it's 6 multiply by what? X Y. Do not forget this.

[00:21:46]Divide by 4 X cubed Y -2L.

[00:22:03]So grade eight step by step. Okay.

[00:22:10]But I cannot do that. I want to show you.

[00:22:14]So 2 exponent 3 2 exponent 3 is 8. Okay.

[00:22:19]So this will be 8 x exponent 6 * x exponent 6 + 1* y. Okay.

[00:22:39]You could divide by 4 exponent 3 y2 step by step.

[00:22:53]Divide that number 8 / 4.

[00:23:05]So this will be 7 - 3 * y exponent 1us open bracketus.

[00:23:27]Therefore the answer in this case it will be what? 2 exponent what? 7 - 3 is 4. Why?

[00:23:35]1 - - 2 it will be equals to 3. So this will be your what? Your answer.

[00:23:44]Okay.

[00:23:49]Let's do example number three.

[00:23:53]Example number three.

[00:24:00]in 33 + 1 exponent 0. Sorry for that. Sorry for this brackets. Sorry.

[00:24:17]3 + 1 exponent 0 + 4 simplify.

[00:24:26]Okay.

[00:24:29]like times expressions.

[00:24:46]constantly.

[00:24:54]It will be 3 + 1 3 + 1 which is 4 exponent 0. Okay. + 4 + 4 which is equals to 5.

[00:25:19]Let's do example number four.

[00:25:22]Example number four.

[00:25:25]If ever you are given um uh 3 - 3 x to the power 4 a to ^ 3 b ^ 1 * -2 to the power or -2 a exponent 2 b exponent 4 all divided by all divided by 2 x a b in this case they're saying simplify -3 X exponent 4 A exponent 3 B multiply by multiplication multiply by what -2 a^ 2 B exponent 4 / 2 X a B simpl only and then you try to uh simplify only 2 minutes you try to simplify.

[00:27:09]I hope We are in my eyes.

[00:27:43]for Italian color.

[00:28:09]All right.

[00:28:32]Um We need to multiply.

[00:28:45]Okay.

[00:29:00]Okay.

[00:29:06]Six. positive six a* a base 3 + 2 5 B exponent.

[00:29:44]So 1 + 4 5 / by what? 2x AB equal to grade 8 before the variables / 2 is 3.

[00:30:10]X exponent 4. x exponent a same base you subtract the exponents a - oh 5 - 1 exponent a four same thing applies to b it will be B 5 - 1 is 4. So this will be your answer.

[00:30:49]Okay.

[00:30:54]Number five.

[00:31:01]That one you got? Um 8 8 ab squ / 2 + a² b square close brackets divide by what? 2.

[00:31:45]Simplify this a² / 2 + inside the bracket a² b² close bracket.

[00:31:56]Okay.

[00:31:59]Remove exponent exponent 1* 2 is 2. So 8 exponent 2 8 exponent 2 a² b²ide by two plusatively made a mistakeatively addition It's negative what a 2 b 2 / what? 2 equal to 8 2 8 64.

[00:33:06]Okay. So 64 / 2.

[00:33:12]So 64 / 22.

[00:33:20]So basically it will be 32.

[00:33:33]/ 2 - a^ 2 b^ 2 / 2 fractions fractions.

[00:33:54]We just subtract the numerators.

[00:34:01]A2= 64us 64 A 2 B 2 - A 2 B 2 64 A 2 B 2 - A 2 B square 3 A 2 like the coefficient.

[00:34:54]All right.

[00:34:56]Simplify the following.

[00:35:00]So I could simplify a x exponent 4 to the^ 5 b 3 exponent 2 to the^ 3 c 4 * 57 a b exponent zero G you know y exponent 11 / y exponent 7 inside the bracket what squared what we simplify that's saying we need to simplify this okay so when we simplify this we are going to apply the laws of exponents number one power of a power Okay, this is a power of a power of a power. What do we do?

[00:36:07]Exponent power x 4* 5 x exponent what? X exponent what? 20 still the same power of a power.

[00:36:28]3* 2* 3 exponent 3 27. So this will be 27.

[00:36:48]27 what? X exponent what? 6 18 number three in four * 57 AB inside the bracket to the power of Z any number to the power.

[00:37:15]So it will be four * 1 which is equals to 4 in power of a power but at the same time we are dividing the same base. Okay when we divide the same base we subtract the what the exponents. So y 11 - 7 inside the bracket squar equal to y 11 - 7 11 - 7 what do we get 4 exponent 2 power of a power 2 * 4 is 8. So y it is y exponent 8 is the answer.

[00:38:04]So one mark two marks one marks.

[00:38:22]So five marks in total.

[00:38:32]So exponent grade 11 and grade 10. Thank you very much.

[00:38:56]I practice grade eight. I practice subject next month exam.

[00:39:32]Champ really loves you. Sharp. Sharp.

[00:39:36]Shalom.