WEBVTT 00:00:05.000 --> 00:00:09.160 Okay, going back to third grade. 00:00:13.180 --> 00:00:14.680 Maybe second grade. 00:00:19.040 --> 00:00:21.940 What does 3 times 4 mean? 00:00:22.920 --> 00:00:24.000 Not what it is. 00:00:24.460 --> 00:00:26.760 Three plus three plus three plus three. 00:00:27.220 --> 00:00:30.840 Three plus three plus three. 00:00:30.860 --> 00:00:31.760 Four plus three. 00:00:31.520 --> 00:00:32.420 Four plus three. 00:00:32.300 --> 00:00:33.200 Four plus three. 00:00:32.620 --> 00:00:33.520 Four plus three. 00:00:33.040 --> 00:00:34.000 What does that mean in general? 00:00:34.600 --> 00:00:35.720 Four plus four plus four. 00:00:36.180 --> 00:00:37.480 4 plus 4. 00:00:40.640 --> 00:00:43.040 Multiplication is just repeated. 00:00:43.500 --> 00:00:44.400 It is. 00:00:44.960 --> 00:00:45.860 Okay. 00:00:46.640 --> 00:00:51.980 Just for fun, what does x times y mean? 00:00:51.980 --> 00:01:01.740 x plus x plus x, repeated y times. 00:01:03.440 --> 00:01:04.340 How many times? 00:01:04.300 --> 00:01:05.480 Y times. 00:01:07.400 --> 00:01:09.160 Hence the word times, right? 00:01:14.700 --> 00:01:15.760 Or it could mean, 00:01:17.980 --> 00:01:20.780 Y plus Y plus Y. 00:01:23.420 --> 00:01:24.380 Next time. 00:01:26.200 --> 00:01:30.880 Now we're going to, I don't know, fifth grade. 00:01:31.940 --> 00:01:32.840 Fifth grade. 00:01:32.760 --> 00:01:34.140 Maybe like 8th grade? 00:01:34.580 --> 00:01:35.480 8th grade? 00:01:35.400 --> 00:01:36.840 Maybe like 10th grade. 00:01:37.440 --> 00:01:38.340 Are you sure? 00:01:38.140 --> 00:01:41.420 What does 3 to the power of 4 mean? 00:01:41.980 --> 00:01:44.440 3 times 3 times 3 times 3. 00:01:48.360 --> 00:01:49.260 4? 00:01:50.640 --> 00:01:51.540 Uh... 00:01:51.400 --> 00:01:53.040 That's it. There is no more. 00:01:53.880 --> 00:01:54.780 Okay. 00:01:56.960 --> 00:01:58.900 Exponents is just repeated? 00:01:59.540 --> 00:02:00.440 Multiplication. 00:02:00.280 --> 00:02:01.180 Multiplication. 00:02:01.880 --> 00:02:10.445 Okay. Because of that, we got lots of rules. Or laws, whatever you want to call 00:02:10.445 --> 00:02:11.195 them. 00:02:13.200 --> 00:02:18.740 Did you guys learn exponent laws last year? 00:02:21.020 --> 00:02:21.920 Sorta. 00:02:23.760 --> 00:02:24.660 Sorta. 00:02:26.920 --> 00:02:35.080 How could I rewrite this? Three to the fifth times three to the fourth is three to 00:02:35.080 --> 00:02:36.040 the ninth. 00:02:37.080 --> 00:02:40.400 Why is that? Because five plus four is nine. 00:02:41.600 --> 00:02:49.820 Right, so 3 to the 5th is 3 times 3 times 3 times 3 times 3. 00:02:49.820 --> 00:02:57.380 This is the same multiplication times 3 times 3 times 3 times 3 00:02:59.280 --> 00:03:04.620 Okay, which is 3 to the 9th 00:03:06.920 --> 00:03:14.900 It's 3 to the 5th times 3 to the 4th is 3 to the 5 plus 4 00:03:16.680 --> 00:03:19.560 Which is 3 to the 9th, okay 00:03:19.820 --> 00:03:36.460 Our first law is x to the a times x to the b equals x to the a plus b. 00:03:40.140 --> 00:03:41.040 Very important. 00:03:43.820 --> 00:03:48.200 They must have the same base, right? 00:03:50.280 --> 00:03:53.560 If it was X to the A times Y to the B 00:03:54.980 --> 00:03:57.820 We could do nothing with it so they got to have the same base 00:04:01.260 --> 00:04:02.160 I 00:04:02.840 --> 00:04:04.540 Don't know if I mentioned this but 00:04:07.740 --> 00:04:09.680 This is called the base 00:04:13.740 --> 00:04:17.220 This value is called the exponent, or the power. 00:04:19.320 --> 00:04:20.600 Or we call it the power. 00:04:27.540 --> 00:04:36.160 The way we say it would be x to the 8th power, 00:04:37.100 --> 00:04:41.220 or just x to the 8th, x to the 8th, 00:04:43.440 --> 00:05:03.460 When the exponent is 2, we also say x squared. Do not say x 2. 00:05:03.460 --> 00:05:11.520 say this x to the power of 2 when there happens to be a 2 we also call it x 00:05:11.520 --> 00:05:33.440 squared squared don't ever say x 2 ok it's x to the second power x to the 00:05:46.840 --> 00:05:51.845 The directions are to simplify, not solve, because this is an expression rather than 00:05:51.845 --> 00:05:52.595 an equation. 00:05:53.200 --> 00:05:54.100 Solve? 00:05:54.680 --> 00:05:55.580 Simply multiply. 00:05:55.600 --> 00:05:56.640 Definitely not be solved. 00:05:56.820 --> 00:05:57.720 Why would it not be solved? 00:05:57.740 --> 00:05:58.640 It's not an equation. 00:05:59.380 --> 00:06:00.280 It's not a equation. 00:06:00.880 --> 00:06:02.300 We don't solve expressions. 00:06:02.300 --> 00:06:17.720 it could be simplified typically. Okay and what are we gonna do first? Okay this is 00:06:17.720 --> 00:06:25.640 important. Terms in algebra are things separated by addition. There's only one 00:06:25.640 --> 00:06:32.660 term here that whole thing is a term okay so we're not combining like terms 00:06:33.300 --> 00:06:42.440 we're just simplifying it okay before we use this law what do we need to do first 00:06:45.240 --> 00:06:51.920 Put the factors with the same bases next to each other. 00:06:51.920 --> 00:06:59.737 Rewrite the product as x to the fifth times x cubed times y to the fourth times y to 00:06:59.737 --> 00:07:00.560 the tenth. 00:07:00.560 --> 00:07:07.820 And what law or what property allows us to just switch the order of this? 00:07:08.520 --> 00:07:09.420 Commutative. 00:07:09.940 --> 00:07:12.120 Commutative property of? 00:07:13.260 --> 00:07:14.160 Multiplication. 00:07:13.740 --> 00:07:14.640 Multiplication. 00:07:15.060 --> 00:07:15.960 OK. 00:07:19.020 --> 00:07:23.520 We could switch the order of multiplication by the commutative property. 00:07:24.280 --> 00:07:41.780 The result is x to the eighth times y to the fourteenth. 00:07:42.460 --> 00:07:47.680 Okay, when you're doing these, do we need to show this step? 00:07:48.800 --> 00:07:49.700 Not really. 00:07:49.620 --> 00:07:50.520 No. 00:07:50.300 --> 00:07:51.320 We can do that in our head. 00:07:52.100 --> 00:07:53.500 Do we need to show this step? 00:07:53.720 --> 00:07:54.620 No. 00:07:54.480 --> 00:07:55.380 Not really. 00:07:55.980 --> 00:08:06.180 We will need to show this step in cases like x to the a times x to the fifth. 00:08:07.980 --> 00:08:09.500 Rewrite this as x to the a plus 5. 00:08:09.880 --> 00:08:10.860 8 plus 5. 00:08:10.920 --> 00:08:11.820 8 plus 5. 00:08:11.720 --> 00:08:12.980 There's no other way to write that. 00:08:14.060 --> 00:08:16.840 OK, so definitely in those cases, 00:08:17.560 --> 00:08:19.540 we have a variable there instead of just a number. 00:08:20.640 --> 00:08:23.500 But otherwise, you can skip this step, skip this step. 00:08:24.860 --> 00:08:26.260 And a lot of times, just do it right in your head, 00:08:26.440 --> 00:08:27.340 just like that. 00:08:40.040 --> 00:08:42.040 What do we do first here? 00:08:44.240 --> 00:08:53.180 Okay, whenever we have addition, okay, to use the laws we just learned, it has to be 00:08:53.180 --> 00:08:54.080 all multiplication. 00:08:54.000 --> 00:08:56.960 So we do need to use the distributive property. 00:08:57.060 --> 00:08:59.200 What's the real name of the distributive property? 00:08:59.980 --> 00:09:02.480 Or the full name I should say. 00:09:05.980 --> 00:09:10.985 The distributive property of multiplication, this is the property of this 00:09:10.985 --> 00:09:11.735 multiplication 00:09:11.440 --> 00:09:14.780 right here, over addition. 00:09:14.980 --> 00:09:17.980 So it's the distributive property of multiplication over addition. 00:09:18.440 --> 00:09:20.140 So we distribute over that addition. 00:09:35.600 --> 00:09:37.000 And 00:09:40.100 --> 00:09:43.380 And now we use the law. 00:09:43.520 --> 00:09:45.540 You can rearrange everything. 00:09:45.840 --> 00:09:47.140 You don't have to. 00:09:48.200 --> 00:09:54.653 Multiply the coefficients and add exponents on like bases: 6x to the eleventh y 00:09:54.653 --> 00:09:58.340 squared plus 8x to the fifth y cubed. 00:09:58.340 --> 00:10:02.060 And can we add in? 00:10:03.460 --> 00:10:04.360 No. 00:10:04.180 --> 00:10:06.800 No, these are not like terms. 00:10:07.800 --> 00:10:11.480 Like terms must have the same variables raised to the same powers. 00:10:11.480 --> 00:10:14.540 variables to the same exact powers. 00:10:16.660 --> 00:10:19.620 Otherwise you can't combine them by adding them. 00:10:20.240 --> 00:10:21.460 They're not like terms. 00:10:36.420 --> 00:10:40.360 Now we are dividing two powers with the same base. 00:10:45.800 --> 00:10:48.300 What is this going to be? 00:10:49.020 --> 00:10:50.406 Three to the sixth divided by three to the fourth is three to the six minus four, or 00:10:50.406 --> 00:10:51.156 three squared. 00:10:51.260 --> 00:10:55.420 3 to the power of 6 minus 4. 00:10:56.920 --> 00:11:01.220 Which is 3 to the power of 2. 00:11:01.460 --> 00:11:03.400 Why is that? Why are we going to subtract? 00:11:06.140 --> 00:11:12.060 If the multiplication has a win dividing the opposite to use in fact. 00:11:12.700 --> 00:11:16.320 Oh yeah, that would logically make sense. But why is that? 00:11:21.820 --> 00:11:30.060 Four of the factors cancel, leaving two factors of 3 in the numerator. 00:11:40.420 --> 00:11:49.280 I like that you don't really need to write this step 00:11:50.060 --> 00:12:02.660 The quotient rule is x to the a divided by x to the b equals x to the a minus b. 00:12:02.660 --> 00:12:03.560 one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, 00:12:02.680 --> 00:12:06.780 one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, one, 00:12:06.780 --> 00:12:13.580 divided by x to the b. When you solve problems like this you just leave them in 00:12:13.580 --> 00:12:14.380 their exponent 00:12:14.380 --> 00:12:18.756 form right you don't like simplify further. You can't you mean multiply it out yeah 00:12:18.756 --> 00:12:19.506 because it's 00:12:19.340 --> 00:12:24.236 just a number all right there's no like hard and fast rule you could multiply it out 00:12:24.236 --> 00:12:25.100 you could just 00:12:25.100 --> 00:12:32.645 leave it okay um I mean you definitely could write this as nine most of our 00:12:32.645 --> 00:12:34.060 expressions are contained 00:12:34.060 --> 00:12:42.460 variables so either way we're practicing the rules there's no right this is the 00:12:42.460 --> 00:12:49.440 same thing as this just written in two different ways okay so the lot X to the 00:12:49.440 --> 00:12:55.620 A divided by X to the B as long as they have the same base now we no longer have 00:12:55.620 --> 00:13:02.940 a denominator. 00:13:02.940 --> 00:13:12.900 By the quotient rule, x to the fourth divided by x to the sixth becomes x to the 00:13:12.900 --> 00:13:14.560 negative second power. 00:13:14.560 --> 00:13:33.220 what in the world a negative we can and what does this even mean like that why 00:13:33.220 --> 00:13:43.380 is that that's true but why is that it's like you have to move it down to make it 00:13:43.380 --> 00:13:45.740 positive. But I'm there now. 00:13:46.120 --> 00:13:49.440 No, because like, there's like, like, I know, like in practice, 00:13:49.640 --> 00:13:50.540 I can like move it down. 00:13:51.040 --> 00:13:52.320 Just move stuff down. 00:13:54.800 --> 00:13:56.960 Right? Isn't that how it works? 00:13:58.280 --> 00:14:00.480 Sort of. Yes. 00:14:02.220 --> 00:14:04.620 I like that. So 00:14:17.160 --> 00:14:28.020 After common factors cancel, we have 1 divided by x times x, or 1 over x squared. 00:14:29.800 --> 00:14:35.329 The negative-exponent rule is x to the negative a equals 1 divided by x to the 00:14:35.329 --> 00:14:36.079 positive a. 00:14:38.660 --> 00:14:48.980 x to the negative a is 1 divided by x to the positive a. 00:14:51.240 --> 00:14:52.480 Very important. 00:14:58.520 --> 00:15:04.160 Assume none of the variables are zero. 00:15:05.680 --> 00:15:11.477 That's important because we can't necessarily simplify but we're going to assume 00:15:11.477 --> 00:15:12.227 they're 00:15:11.960 --> 00:15:12.860 never zero. 00:15:14.260 --> 00:15:15.560 So what now? 00:15:22.520 --> 00:15:25.040 Well we could break it up like this. 00:15:26.220 --> 00:15:27.380 We're not going to. 00:15:28.380 --> 00:15:29.860 We're going to do this part in our head. 00:15:38.620 --> 00:15:42.740 And then we could use that law for each one individually. 00:15:48.460 --> 00:15:56.280 Using the quotient rule gives one fourth times x to the three minus one times y to 00:15:56.280 --> 00:15:58.120 the five minus eight. 00:16:07.780 --> 00:16:11.480 Okay, and we're typically not going to leave anything with negative exponents. 00:16:13.000 --> 00:16:15.960 So we don't want this as our final answer. 00:16:15.960 --> 00:16:17.920 We need to get rid of the negative exponent. 00:16:17.920 --> 00:16:28.600 This becomes one fourth times x squared times 1 over y cubed. 00:16:32.500 --> 00:16:39.920 The final simplified form is x squared over 4y cubed. 00:16:39.920 --> 00:16:57.880 get that that would be our final simplified form okay just kind of a 00:16:57.880 --> 00:17:05.860 shortcut where we don't have to go through all these steps will be as a 00:17:05.860 --> 00:17:21.120 know shortcuts. Just like we do like this, we rarely write this as 2 over 2 times 4, 00:17:22.900 --> 00:17:28.160 2 over 2 times 1 over 4. 2 over 2 is 1. 00:17:33.040 --> 00:17:34.520 What do we normally do? 00:17:36.060 --> 00:17:39.060 Reduce 2 over 8 to one fourth, then cancel common variable factors. 00:17:39.720 --> 00:17:40.620 And we get a 2. 00:17:41.760 --> 00:17:42.660 And we have 4. 00:17:43.380 --> 00:17:44.280 And you just write 1 fourth. 00:17:45.760 --> 00:17:47.560 So we're going to do the same thing with variables as well. 00:17:47.700 --> 00:17:48.600 So first we can do that. 00:17:48.440 --> 00:17:53.287 And this only works if everything is multiplication. There's addition. Don't ever do 00:17:53.287 --> 00:17:54.037 this 00:17:54.680 --> 00:17:56.920 Okay, so we just go one 00:17:57.680 --> 00:17:58.580 fourth 00:18:00.120 --> 00:18:03.894 Cancel one x factor to leave x squared, and cancel five y factors to leave y cubed 00:18:03.894 --> 00:18:04.644 in the denominator. 00:18:06.320 --> 00:18:11.200 Five of these simplify with five of these and we get y cubed 00:18:13.260 --> 00:18:22.180 1 times x squared times 1 is x squared over 4 times 1 times y cubed 4y cubed. 00:18:23.920 --> 00:18:29.509 When numerator and denominator are products, simplify variable factors just as you 00:18:29.509 --> 00:18:30.440 simplify fractions. 00:18:30.440 --> 00:18:32.480 simplify just like we simplify fractions. 00:18:35.620 --> 00:18:37.800 Okay, you can do either way. 00:18:39.080 --> 00:18:44.640 But it's usually fastest if we do it this way. 00:18:46.380 --> 00:18:47.780 Okay. 00:18:47.780 --> 00:18:54.400 Now we have a product raised to a power. 00:18:59.620 --> 00:19:01.460 If I wrote it out, it would be what? 00:19:01.660 --> 00:19:06.200 3x times 3x times 3x times 3x. 00:19:06.240 --> 00:19:09.860 Agree? And then if you want, you could rearrange it. 00:19:14.880 --> 00:19:20.100 And then this is 3 to the fourth x to the fourth. 00:19:24.840 --> 00:19:31.695 The power-of-a-product rule is open parenthesis xy close parenthesis to the a equals 00:19:31.695 --> 00:19:36.440 x to the a times y to the a. 00:19:36.440 --> 00:19:37.340 become? 00:19:36.900 --> 00:19:49.440 X to the A, don't say XA. Y to the A, or Y to the A power. 00:19:51.960 --> 00:19:55.700 This is when we have a product inside an exponent. 00:19:57.400 --> 00:20:04.940 You raise every one of the things inside to the power of whatever that exponent is. 00:20:08.200 --> 00:20:12.000 And we might as well do one more before we do some more examples. 00:20:26.680 --> 00:20:29.660 A power raised to a power multiplies the exponents. 00:20:29.880 --> 00:20:31.880 The entire thing is raised to an exponent. 00:20:34.800 --> 00:20:42.227 We got, if I wrote it out, it's 3 squared times 3 squared times 3 squared times 3 00:20:42.227 --> 00:20:42.977 squared. 00:20:45.740 --> 00:20:47.300 Now they all have the same base. 00:20:48.540 --> 00:20:50.900 So it's 3 to the 2 times 2 times 2. 00:20:51.840 --> 00:20:52.780 Plus 2. 00:20:53.040 --> 00:20:53.980 Plus 2. 00:20:54.180 --> 00:20:55.080 Plus 2. 00:20:54.720 --> 00:21:03.420 plus 2, which is 3 to the 2 times 4 repeated addition. 00:21:06.060 --> 00:21:07.980 Which we end up just multiplying these exponents. 00:21:09.140 --> 00:21:10.640 The power-to-a-power rule is open parenthesis x to the a close parenthesis to the b 00:21:10.640 --> 00:21:11.390 equals x to the ab. 00:21:13.600 --> 00:21:29.140 So our next law is x to the a to the power of b is x to the a times b. 00:21:46.560 --> 00:21:49.520 And actually I meant one more. 00:21:52.100 --> 00:21:58.797 The power-of-a-quotient rule is open parenthesis x over y close parenthesis to the a 00:21:58.797 --> 00:22:03.580 equals x to the a over y to the a. 00:22:03.860 --> 00:22:08.434 So if you have a quotient inside an exponent, the numerator gets the power and the 00:22:08.434 --> 00:22:09.184 denominator 00:22:09.320 --> 00:22:25.660 Okay, let's do some examples. 00:22:25.660 --> 00:22:26.560 Yes. 00:23:04.100 --> 00:23:06.100 Apply the outer third power to the numerator and denominator. 00:23:08.520 --> 00:23:10.180 What rule are we going to use first? 00:23:16.240 --> 00:23:19.380 There's no addition, we're definitely not distributing anything. 00:23:21.700 --> 00:23:28.480 So, overall we have a quotient, okay, inside the exponent. 00:23:29.440 --> 00:23:31.285 This becomes open parenthesis 3x squared y cubed close parenthesis cubed over open 00:23:31.285 --> 00:23:32.420 parenthesis 2z to the fourth close parenthesis cubed. 00:23:36.740 --> 00:23:47.047 So it becomes 3x squared y cubed to the third power, 2z to the fourth to the third 00:23:47.047 --> 00:23:47.797 power. 00:23:50.860 --> 00:23:53.660 And now within the numerator and within the denominator, 00:23:53.760 --> 00:23:59.840 we have a product to a power, a product to a power. 00:24:03.220 --> 00:24:07.300 Apply the third power to every factor in the numerator and denominator. 00:24:07.940 --> 00:24:10.820 X squared to the power of three, 00:24:11.300 --> 00:24:13.920 Y cubed to the power of three, 00:24:15.380 --> 00:24:16.780 two to the power of three, 00:24:17.620 --> 00:24:20.720 Z to the fourth power of three. 00:24:32.260 --> 00:24:38.300 Multiply the exponents in each power-to-a-power expression. 00:24:38.300 --> 00:24:39.200 a power. 00:24:39.600 --> 00:24:41.320 Base exponent raised to a power. 00:24:43.100 --> 00:24:44.660 And we multiply those. 00:24:46.580 --> 00:24:59.980 So it's 3 cubed x squared to the 2 times 3, y to the 3 times 3, 4 times 3. 00:25:01.180 --> 00:25:03.380 You can't just do that multiplication in your head. 00:25:03.380 --> 00:25:11.900 You don't have to write that part out. 00:25:20.060 --> 00:25:23.720 You could multiply out the 3's. 00:25:24.540 --> 00:25:36.640 The simplified result is 27x to the sixth y to the ninth over 8z to the twelfth. 00:25:36.700 --> 00:25:38.880 And then do we need to simplify anything? 00:25:40.160 --> 00:25:47.164 No, these are, the coefficients are not going to reduce and they don't have any of 00:25:47.164 --> 00:25:48.040 the same 00:25:48.040 --> 00:25:49.600 variables so there's no more simplification. 00:25:50.100 --> 00:25:51.000 This would be it. 00:26:08.100 --> 00:26:10.080 questions on that? 00:26:10.500 --> 00:26:12.320 are we done? 00:26:14.380 --> 00:26:17.020 not yet, not yet, not yet. 00:26:20.220 --> 00:26:22.000 Let's do a couple more. 00:26:22.000 --> 00:26:38.440 Simplify each base using the quotient rule. 00:26:38.440 --> 00:26:44.940 For x, subtracting a negative exponent gives 4 minus negative 5, or 9. 00:26:44.940 --> 00:26:51.980 is x to the 9. The other way we could do this is to use the 00:26:52.000 --> 00:27:01.988 Equivalently, x to the negative fifth in the denominator becomes x to the fifth in 00:27:01.988 --> 00:27:03.320 the numerator. 00:27:03.840 --> 00:27:12.160 multiplied by the reciprocal of the denominator and x to the fourth times x 00:27:12.390 --> 00:27:25.842 fifth is x to the ninth. Or we could just do this three times x to the four minus 00:27:25.842 --> 00:27:26.592 negative 00:27:26.550 --> 00:27:39.890 The expression becomes 3x to the ninth times y to the negative first. 00:27:45.150 --> 00:27:53.650 With positive exponents, the final answer is 3x to the ninth over y. 00:27:53.650 --> 00:27:56.830 Oh wait, I forgot one major thing. 00:28:04.330 --> 00:28:06.770 What does a zero exponent mean? 00:28:08.930 --> 00:28:10.090 One, why is that? 00:28:12.110 --> 00:28:13.010 I was told. 00:28:13.550 --> 00:28:14.450 You were told? 00:28:14.450 --> 00:28:15.350 Yeah. 00:28:15.530 --> 00:28:18.550 It's correct, but what would be a reason why this would be up? 00:28:19.370 --> 00:28:24.850 When you go up, my exclamation multiply, so if you go down, you divide. 00:28:24.850 --> 00:28:28.450 So much of our 1 is 5, and then you divide by 5 and you get 1. 00:28:29.490 --> 00:28:31.710 OK, I like that. Let's go with 125. 00:28:37.890 --> 00:28:41.010 25, 5, or this is what, 5 cubed, 00:28:41.410 --> 00:28:43.750 5 squared, 5 to the first, 00:28:45.910 --> 00:28:48.930 5 to the 0. You divide, 00:28:49.210 --> 00:28:52.730 you divide, you divide, this becomes 1. Divide by 5. 00:28:52.730 --> 00:29:09.710 OK, anything to the power of zero is one, except zero to the zero is undefined. 00:29:12.250 --> 00:29:15.670 But besides that, anything to the power of zero is one. 00:29:17.590 --> 00:29:18.490 It's very important. 00:29:22.910 --> 00:29:28.841 And if you ever end up with like x to the fourth divided by x to the fourth, 00:29:28.841 --> 00:29:29.591 obviously 00:29:29.170 --> 00:29:31.190 this simplifies to just one, right? 00:29:32.750 --> 00:29:39.058 But if you use our rules, we have four minus four, which is x to the zero, and the 00:29:39.058 --> 00:29:39.808 zero 00:29:39.390 --> 00:29:40.290 is one.