1 00:00:05,000 --> 00:00:09,160 Okay, going back to third grade. 2 00:00:13,180 --> 00:00:14,680 Maybe second grade. 3 00:00:19,040 --> 00:00:21,940 What does 3 times 4 mean? 4 00:00:22,920 --> 00:00:24,000 Not what it is. 5 00:00:24,460 --> 00:00:26,760 Three plus three plus three plus three. 6 00:00:27,220 --> 00:00:30,840 Three plus three plus three. 7 00:00:30,860 --> 00:00:31,760 Four plus three. 8 00:00:31,520 --> 00:00:32,420 Four plus three. 9 00:00:32,300 --> 00:00:33,200 Four plus three. 10 00:00:32,620 --> 00:00:33,520 Four plus three. 11 00:00:33,040 --> 00:00:34,000 What does that mean in general? 12 00:00:34,600 --> 00:00:35,720 Four plus four plus four. 13 00:00:36,180 --> 00:00:37,480 4 plus 4. 14 00:00:40,640 --> 00:00:43,040 Multiplication is just repeated. 15 00:00:43,500 --> 00:00:44,400 It is. 16 00:00:44,960 --> 00:00:45,860 Okay. 17 00:00:46,640 --> 00:00:51,980 Just for fun, what does x times y mean? 18 00:00:51,980 --> 00:01:01,740 x plus x plus x, repeated y times. 19 00:01:03,440 --> 00:01:04,340 How many times? 20 00:01:04,300 --> 00:01:05,480 Y times. 21 00:01:07,400 --> 00:01:09,160 Hence the word times, right? 22 00:01:14,700 --> 00:01:15,760 Or it could mean, 23 00:01:17,980 --> 00:01:20,780 Y plus Y plus Y. 24 00:01:23,420 --> 00:01:24,380 Next time. 25 00:01:26,200 --> 00:01:30,880 Now we're going to, I don't know, fifth grade. 26 00:01:31,940 --> 00:01:32,840 Fifth grade. 27 00:01:32,760 --> 00:01:34,140 Maybe like 8th grade? 28 00:01:34,580 --> 00:01:35,480 8th grade? 29 00:01:35,400 --> 00:01:36,840 Maybe like 10th grade. 30 00:01:37,440 --> 00:01:38,340 Are you sure? 31 00:01:38,140 --> 00:01:41,420 What does 3 to the power of 4 mean? 32 00:01:41,980 --> 00:01:44,440 3 times 3 times 3 times 3. 33 00:01:48,360 --> 00:01:49,260 4? 34 00:01:50,640 --> 00:01:51,540 Uh... 35 00:01:51,400 --> 00:01:53,040 That's it. There is no more. 36 00:01:53,880 --> 00:01:54,780 Okay. 37 00:01:56,960 --> 00:01:58,900 Exponents is just repeated? 38 00:01:59,540 --> 00:02:00,440 Multiplication. 39 00:02:00,280 --> 00:02:01,180 Multiplication. 40 00:02:01,880 --> 00:02:10,445 Okay. Because of that, we got lots of rules. Or laws, whatever you want to call 41 00:02:10,445 --> 00:02:11,195 them. 42 00:02:13,200 --> 00:02:18,740 Did you guys learn exponent laws last year? 43 00:02:21,020 --> 00:02:21,920 Sorta. 44 00:02:23,760 --> 00:02:24,660 Sorta. 45 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 46 00:02:35,080 --> 00:02:36,040 the ninth. 47 00:02:37,080 --> 00:02:40,400 Why is that? Because five plus four is nine. 48 00:02:41,600 --> 00:02:49,820 Right, so 3 to the 5th is 3 times 3 times 3 times 3 times 3. 49 00:02:49,820 --> 00:02:57,380 This is the same multiplication times 3 times 3 times 3 times 3 50 00:02:59,280 --> 00:03:04,620 Okay, which is 3 to the 9th 51 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 52 00:03:16,680 --> 00:03:19,560 Which is 3 to the 9th, okay 53 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. 54 00:03:40,140 --> 00:03:41,040 Very important. 55 00:03:43,820 --> 00:03:48,200 They must have the same base, right? 56 00:03:50,280 --> 00:03:53,560 If it was X to the A times Y to the B 57 00:03:54,980 --> 00:03:57,820 We could do nothing with it so they got to have the same base 58 00:04:01,260 --> 00:04:02,160 I 59 00:04:02,840 --> 00:04:04,540 Don't know if I mentioned this but 60 00:04:07,740 --> 00:04:09,680 This is called the base 61 00:04:13,740 --> 00:04:17,220 This value is called the exponent, or the power. 62 00:04:19,320 --> 00:04:20,600 Or we call it the power. 63 00:04:27,540 --> 00:04:36,160 The way we say it would be x to the 8th power, 64 00:04:37,100 --> 00:04:41,220 or just x to the 8th, x to the 8th, 65 00:04:43,440 --> 00:05:03,460 When the exponent is 2, we also say x squared. Do not say x 2. 66 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 67 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 68 00:05:46,840 --> 00:05:51,845 The directions are to simplify, not solve, because this is an expression rather than 69 00:05:51,845 --> 00:05:52,595 an equation. 70 00:05:53,200 --> 00:05:54,100 Solve? 71 00:05:54,680 --> 00:05:55,580 Simply multiply. 72 00:05:55,600 --> 00:05:56,640 Definitely not be solved. 73 00:05:56,820 --> 00:05:57,720 Why would it not be solved? 74 00:05:57,740 --> 00:05:58,640 It's not an equation. 75 00:05:59,380 --> 00:06:00,280 It's not a equation. 76 00:06:00,880 --> 00:06:02,300 We don't solve expressions. 77 00:06:02,300 --> 00:06:17,720 it could be simplified typically. Okay and what are we gonna do first? Okay this is 78 00:06:17,720 --> 00:06:25,640 important. Terms in algebra are things separated by addition. There's only one 79 00:06:25,640 --> 00:06:32,660 term here that whole thing is a term okay so we're not combining like terms 80 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 81 00:06:45,240 --> 00:06:51,920 Put the factors with the same bases next to each other. 82 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 83 00:06:59,737 --> 00:07:00,560 the tenth. 84 00:07:00,560 --> 00:07:07,820 And what law or what property allows us to just switch the order of this? 85 00:07:08,520 --> 00:07:09,420 Commutative. 86 00:07:09,940 --> 00:07:12,120 Commutative property of? 87 00:07:13,260 --> 00:07:14,160 Multiplication. 88 00:07:13,740 --> 00:07:14,640 Multiplication. 89 00:07:15,060 --> 00:07:15,960 OK. 90 00:07:19,020 --> 00:07:23,520 We could switch the order of multiplication by the commutative property. 91 00:07:24,280 --> 00:07:41,780 The result is x to the eighth times y to the fourteenth. 92 00:07:42,460 --> 00:07:47,680 Okay, when you're doing these, do we need to show this step? 93 00:07:48,800 --> 00:07:49,700 Not really. 94 00:07:49,620 --> 00:07:50,520 No. 95 00:07:50,300 --> 00:07:51,320 We can do that in our head. 96 00:07:52,100 --> 00:07:53,500 Do we need to show this step? 97 00:07:53,720 --> 00:07:54,620 No. 98 00:07:54,480 --> 00:07:55,380 Not really. 99 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. 100 00:08:07,980 --> 00:08:09,500 Rewrite this as x to the a plus 5. 101 00:08:09,880 --> 00:08:10,860 8 plus 5. 102 00:08:10,920 --> 00:08:11,820 8 plus 5. 103 00:08:11,720 --> 00:08:12,980 There's no other way to write that. 104 00:08:14,060 --> 00:08:16,840 OK, so definitely in those cases, 105 00:08:17,560 --> 00:08:19,540 we have a variable there instead of just a number. 106 00:08:20,640 --> 00:08:23,500 But otherwise, you can skip this step, skip this step. 107 00:08:24,860 --> 00:08:26,260 And a lot of times, just do it right in your head, 108 00:08:26,440 --> 00:08:27,340 just like that. 109 00:08:40,040 --> 00:08:42,040 What do we do first here? 110 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 111 00:08:53,180 --> 00:08:54,080 all multiplication. 112 00:08:54,000 --> 00:08:56,960 So we do need to use the distributive property. 113 00:08:57,060 --> 00:08:59,200 What's the real name of the distributive property? 114 00:08:59,980 --> 00:09:02,480 Or the full name I should say. 115 00:09:05,980 --> 00:09:10,985 The distributive property of multiplication, this is the property of this 116 00:09:10,985 --> 00:09:11,735 multiplication 117 00:09:11,440 --> 00:09:14,780 right here, over addition. 118 00:09:14,980 --> 00:09:17,980 So it's the distributive property of multiplication over addition. 119 00:09:18,440 --> 00:09:20,140 So we distribute over that addition. 120 00:09:35,600 --> 00:09:37,000 And 121 00:09:40,100 --> 00:09:43,380 And now we use the law. 122 00:09:43,520 --> 00:09:45,540 You can rearrange everything. 123 00:09:45,840 --> 00:09:47,140 You don't have to. 124 00:09:48,200 --> 00:09:54,653 Multiply the coefficients and add exponents on like bases: 6x to the eleventh y 125 00:09:54,653 --> 00:09:58,340 squared plus 8x to the fifth y cubed. 126 00:09:58,340 --> 00:10:02,060 And can we add in? 127 00:10:03,460 --> 00:10:04,360 No. 128 00:10:04,180 --> 00:10:06,800 No, these are not like terms. 129 00:10:07,800 --> 00:10:11,480 Like terms must have the same variables raised to the same powers. 130 00:10:11,480 --> 00:10:14,540 variables to the same exact powers. 131 00:10:16,660 --> 00:10:19,620 Otherwise you can't combine them by adding them. 132 00:10:20,240 --> 00:10:21,460 They're not like terms. 133 00:10:36,420 --> 00:10:40,360 Now we are dividing two powers with the same base. 134 00:10:45,800 --> 00:10:48,300 What is this going to be? 135 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 136 00:10:50,406 --> 00:10:51,156 three squared. 137 00:10:51,260 --> 00:10:55,420 3 to the power of 6 minus 4. 138 00:10:56,920 --> 00:11:01,220 Which is 3 to the power of 2. 139 00:11:01,460 --> 00:11:03,400 Why is that? Why are we going to subtract? 140 00:11:06,140 --> 00:11:12,060 If the multiplication has a win dividing the opposite to use in fact. 141 00:11:12,700 --> 00:11:16,320 Oh yeah, that would logically make sense. But why is that? 142 00:11:21,820 --> 00:11:30,060 Four of the factors cancel, leaving two factors of 3 in the numerator. 143 00:11:40,420 --> 00:11:49,280 I like that you don't really need to write this step 144 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. 145 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, 146 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, 147 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 148 00:12:13,580 --> 00:12:14,380 their exponent 149 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 150 00:12:18,756 --> 00:12:19,506 because it's 151 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 152 00:12:24,236 --> 00:12:25,100 you could just 153 00:12:25,100 --> 00:12:32,645 leave it okay um I mean you definitely could write this as nine most of our 154 00:12:32,645 --> 00:12:34,060 expressions are contained 155 00:12:34,060 --> 00:12:42,460 variables so either way we're practicing the rules there's no right this is the 156 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 157 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 158 00:12:55,620 --> 00:13:02,940 a denominator. 159 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 160 00:13:12,900 --> 00:13:14,560 negative second power. 161 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 162 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 163 00:13:43,380 --> 00:13:45,740 positive. But I'm there now. 164 00:13:46,120 --> 00:13:49,440 No, because like, there's like, like, I know, like in practice, 165 00:13:49,640 --> 00:13:50,540 I can like move it down. 166 00:13:51,040 --> 00:13:52,320 Just move stuff down. 167 00:13:54,800 --> 00:13:56,960 Right? Isn't that how it works? 168 00:13:58,280 --> 00:14:00,480 Sort of. Yes. 169 00:14:02,220 --> 00:14:04,620 I like that. So 170 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. 171 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 172 00:14:35,329 --> 00:14:36,079 positive a. 173 00:14:38,660 --> 00:14:48,980 x to the negative a is 1 divided by x to the positive a. 174 00:14:51,240 --> 00:14:52,480 Very important. 175 00:14:58,520 --> 00:15:04,160 Assume none of the variables are zero. 176 00:15:05,680 --> 00:15:11,477 That's important because we can't necessarily simplify but we're going to assume 177 00:15:11,477 --> 00:15:12,227 they're 178 00:15:11,960 --> 00:15:12,860 never zero. 179 00:15:14,260 --> 00:15:15,560 So what now? 180 00:15:22,520 --> 00:15:25,040 Well we could break it up like this. 181 00:15:26,220 --> 00:15:27,380 We're not going to. 182 00:15:28,380 --> 00:15:29,860 We're going to do this part in our head. 183 00:15:38,620 --> 00:15:42,740 And then we could use that law for each one individually. 184 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 185 00:15:56,280 --> 00:15:58,120 the five minus eight. 186 00:16:07,780 --> 00:16:11,480 Okay, and we're typically not going to leave anything with negative exponents. 187 00:16:13,000 --> 00:16:15,960 So we don't want this as our final answer. 188 00:16:15,960 --> 00:16:17,920 We need to get rid of the negative exponent. 189 00:16:17,920 --> 00:16:28,600 This becomes one fourth times x squared times 1 over y cubed. 190 00:16:32,500 --> 00:16:39,920 The final simplified form is x squared over 4y cubed. 191 00:16:39,920 --> 00:16:57,880 get that that would be our final simplified form okay just kind of a 192 00:16:57,880 --> 00:17:05,860 shortcut where we don't have to go through all these steps will be as a 193 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, 194 00:17:22,900 --> 00:17:28,160 2 over 2 times 1 over 4. 2 over 2 is 1. 195 00:17:33,040 --> 00:17:34,520 What do we normally do? 196 00:17:36,060 --> 00:17:39,060 Reduce 2 over 8 to one fourth, then cancel common variable factors. 197 00:17:39,720 --> 00:17:40,620 And we get a 2. 198 00:17:41,760 --> 00:17:42,660 And we have 4. 199 00:17:43,380 --> 00:17:44,280 And you just write 1 fourth. 200 00:17:45,760 --> 00:17:47,560 So we're going to do the same thing with variables as well. 201 00:17:47,700 --> 00:17:48,600 So first we can do that. 202 00:17:48,440 --> 00:17:53,287 And this only works if everything is multiplication. There's addition. Don't ever do 203 00:17:53,287 --> 00:17:54,037 this 204 00:17:54,680 --> 00:17:56,920 Okay, so we just go one 205 00:17:57,680 --> 00:17:58,580 fourth 206 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 207 00:18:03,894 --> 00:18:04,644 in the denominator. 208 00:18:06,320 --> 00:18:11,200 Five of these simplify with five of these and we get y cubed 209 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. 210 00:18:23,920 --> 00:18:29,509 When numerator and denominator are products, simplify variable factors just as you 211 00:18:29,509 --> 00:18:30,440 simplify fractions. 212 00:18:30,440 --> 00:18:32,480 simplify just like we simplify fractions. 213 00:18:35,620 --> 00:18:37,800 Okay, you can do either way. 214 00:18:39,080 --> 00:18:44,640 But it's usually fastest if we do it this way. 215 00:18:46,380 --> 00:18:47,780 Okay. 216 00:18:47,780 --> 00:18:54,400 Now we have a product raised to a power. 217 00:18:59,620 --> 00:19:01,460 If I wrote it out, it would be what? 218 00:19:01,660 --> 00:19:06,200 3x times 3x times 3x times 3x. 219 00:19:06,240 --> 00:19:09,860 Agree? And then if you want, you could rearrange it. 220 00:19:14,880 --> 00:19:20,100 And then this is 3 to the fourth x to the fourth. 221 00:19:24,840 --> 00:19:31,695 The power-of-a-product rule is open parenthesis xy close parenthesis to the a equals 222 00:19:31,695 --> 00:19:36,440 x to the a times y to the a. 223 00:19:36,440 --> 00:19:37,340 become? 224 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. 225 00:19:51,960 --> 00:19:55,700 This is when we have a product inside an exponent. 226 00:19:57,400 --> 00:20:04,940 You raise every one of the things inside to the power of whatever that exponent is. 227 00:20:08,200 --> 00:20:12,000 And we might as well do one more before we do some more examples. 228 00:20:26,680 --> 00:20:29,660 A power raised to a power multiplies the exponents. 229 00:20:29,880 --> 00:20:31,880 The entire thing is raised to an exponent. 230 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 3 231 00:20:42,227 --> 00:20:42,977 squared. 232 00:20:45,740 --> 00:20:47,300 Now they all have the same base. 233 00:20:48,540 --> 00:20:50,900 So it's 3 to the 2 times 2 times 2. 234 00:20:51,840 --> 00:20:52,780 Plus 2. 235 00:20:53,040 --> 00:20:53,980 Plus 2. 236 00:20:54,180 --> 00:20:55,080 Plus 2. 237 00:20:54,720 --> 00:21:03,420 plus 2, which is 3 to the 2 times 4 repeated addition. 238 00:21:06,060 --> 00:21:07,980 Which we end up just multiplying these exponents. 239 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 240 00:21:10,640 --> 00:21:11,390 equals x to the ab. 241 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. 242 00:21:46,560 --> 00:21:49,520 And actually I meant one more. 243 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 244 00:21:58,797 --> 00:22:03,580 equals x to the a over y to the a. 245 00:22:03,860 --> 00:22:08,434 So if you have a quotient inside an exponent, the numerator gets the power and the 246 00:22:08,434 --> 00:22:09,184 denominator 247 00:22:09,320 --> 00:22:25,660 Okay, let's do some examples. 248 00:22:25,660 --> 00:22:26,560 Yes. 249 00:23:04,100 --> 00:23:06,100 Apply the outer third power to the numerator and denominator. 250 00:23:08,520 --> 00:23:10,180 What rule are we going to use first? 251 00:23:16,240 --> 00:23:19,380 There's no addition, we're definitely not distributing anything. 252 00:23:21,700 --> 00:23:28,480 So, overall we have a quotient, okay, inside the exponent. 253 00:23:29,440 --> 00:23:31,285 This becomes open parenthesis 3x squared y cubed close parenthesis cubed over open 254 00:23:31,285 --> 00:23:32,420 parenthesis 2z to the fourth close parenthesis cubed. 255 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 256 00:23:47,047 --> 00:23:47,797 power. 257 00:23:50,860 --> 00:23:53,660 And now within the numerator and within the denominator, 258 00:23:53,760 --> 00:23:59,840 we have a product to a power, a product to a power. 259 00:24:03,220 --> 00:24:07,300 Apply the third power to every factor in the numerator and denominator. 260 00:24:07,940 --> 00:24:10,820 X squared to the power of three, 261 00:24:11,300 --> 00:24:13,920 Y cubed to the power of three, 262 00:24:15,380 --> 00:24:16,780 two to the power of three, 263 00:24:17,620 --> 00:24:20,720 Z to the fourth power of three. 264 00:24:32,260 --> 00:24:38,300 Multiply the exponents in each power-to-a-power expression. 265 00:24:38,300 --> 00:24:39,200 a power. 266 00:24:39,600 --> 00:24:41,320 Base exponent raised to a power. 267 00:24:43,100 --> 00:24:44,660 And we multiply those. 268 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. 269 00:25:01,180 --> 00:25:03,380 You can't just do that multiplication in your head. 270 00:25:03,380 --> 00:25:11,900 You don't have to write that part out. 271 00:25:20,060 --> 00:25:23,720 You could multiply out the 3's. 272 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. 273 00:25:36,700 --> 00:25:38,880 And then do we need to simplify anything? 274 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 275 00:25:47,164 --> 00:25:48,040 the same 276 00:25:48,040 --> 00:25:49,600 variables so there's no more simplification. 277 00:25:50,100 --> 00:25:51,000 This would be it. 278 00:26:08,100 --> 00:26:10,080 questions on that? 279 00:26:10,500 --> 00:26:12,320 are we done? 280 00:26:14,380 --> 00:26:17,020 not yet, not yet, not yet. 281 00:26:20,220 --> 00:26:22,000 Let's do a couple more. 282 00:26:22,000 --> 00:26:38,440 Simplify each base using the quotient rule. 283 00:26:38,440 --> 00:26:44,940 For x, subtracting a negative exponent gives 4 minus negative 5, or 9. 284 00:26:44,940 --> 00:26:51,980 is x to the 9. The other way we could do this is to use the 285 00:26:52,000 --> 00:27:01,988 Equivalently, x to the negative fifth in the denominator becomes x to the fifth in 286 00:27:01,988 --> 00:27:03,320 the numerator. 287 00:27:03,840 --> 00:27:12,160 multiplied by the reciprocal of the denominator and x to the fourth times x 288 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 289 00:27:25,842 --> 00:27:26,592 negative 290 00:27:26,550 --> 00:27:39,890 The expression becomes 3x to the ninth times y to the negative first. 291 00:27:45,150 --> 00:27:53,650 With positive exponents, the final answer is 3x to the ninth over y. 292 00:27:53,650 --> 00:27:56,830 Oh wait, I forgot one major thing. 293 00:28:04,330 --> 00:28:06,770 What does a zero exponent mean? 294 00:28:08,930 --> 00:28:10,090 One, why is that? 295 00:28:12,110 --> 00:28:13,010 I was told. 296 00:28:13,550 --> 00:28:14,450 You were told? 297 00:28:14,450 --> 00:28:15,350 Yeah. 298 00:28:15,530 --> 00:28:18,550 It's correct, but what would be a reason why this would be up? 299 00:28:19,370 --> 00:28:24,850 When you go up, my exclamation multiply, so if you go down, you divide. 300 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. 301 00:28:29,490 --> 00:28:31,710 OK, I like that. Let's go with 125. 302 00:28:37,890 --> 00:28:41,010 25, 5, or this is what, 5 cubed, 303 00:28:41,410 --> 00:28:43,750 5 squared, 5 to the first, 304 00:28:45,910 --> 00:28:48,930 5 to the 0. You divide, 305 00:28:49,210 --> 00:28:52,730 you divide, you divide, this becomes 1. Divide by 5. 306 00:28:52,730 --> 00:29:09,710 OK, anything to the power of zero is one, except zero to the zero is undefined. 307 00:29:12,250 --> 00:29:15,670 But besides that, anything to the power of zero is one. 308 00:29:17,590 --> 00:29:18,490 It's very important. 309 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, 310 00:29:28,841 --> 00:29:29,591 obviously 311 00:29:29,170 --> 00:29:31,190 this simplifies to just one, right? 312 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 313 00:29:39,058 --> 00:29:39,808 zero 314 00:29:39,390 --> 00:29:40,290 is one.