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[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:01.23,0:00:05.60,Default,,0000,0000,0000,,Welcome to the presentation\Non level one exponent rules.
Dialogue: 0,0:00:05.60,0:00:08.15,Default,,0000,0000,0000,,Let's get started\Nwith some problems.
Dialogue: 0,0:00:08.15,0:00:12.87,Default,,0000,0000,0000,,So if I were to ask you what 2\N-- that's a little fatter than
Dialogue: 0,0:00:12.87,0:00:15.08,Default,,0000,0000,0000,,I wanted it to be, but let's\Nkeep it fat so it doesn't look
Dialogue: 0,0:00:15.08,0:00:20.26,Default,,0000,0000,0000,,strange -- 2 the third times --\Nand dot is another way of
Dialogue: 0,0:00:20.26,0:00:23.23,Default,,0000,0000,0000,,saying times -- if I were to\Nask you what 2 to the third
Dialogue: 0,0:00:23.23,0:00:27.82,Default,,0000,0000,0000,,times 2 to the fifth is, how\Nwould you figure that out?
Dialogue: 0,0:00:27.82,0:00:30.61,Default,,0000,0000,0000,,Actually, let me use a skinnier\Npen because that does look bad.
Dialogue: 0,0:00:30.61,0:00:35.12,Default,,0000,0000,0000,,So, 2 to the third\Ntimes 2 to the fifth.
Dialogue: 0,0:00:35.12,0:00:37.61,Default,,0000,0000,0000,,Well there's one way that I\Nthink you do know how to do it.
Dialogue: 0,0:00:37.61,0:00:42.15,Default,,0000,0000,0000,,You could figure out that\N2 to the third is 9, and
Dialogue: 0,0:00:42.15,0:00:45.38,Default,,0000,0000,0000,,that 2 to the fifth is 32.
Dialogue: 0,0:00:45.38,0:00:46.84,Default,,0000,0000,0000,,And then you could\Nmultiply them.
Dialogue: 0,0:00:46.84,0:00:54.01,Default,,0000,0000,0000,,And 8 times 32 is 240,\Nplus it's 256, right?
Dialogue: 0,0:00:54.01,0:00:55.53,Default,,0000,0000,0000,,You could do it that way.
Dialogue: 0,0:00:55.53,0:00:58.55,Default,,0000,0000,0000,,That's reasonable because it's\Nnot that hard to figure out 2
Dialogue: 0,0:00:58.55,0:01:00.52,Default,,0000,0000,0000,,to the third is and what\N2 to the fifth is.
Dialogue: 0,0:01:00.52,0:01:03.15,Default,,0000,0000,0000,,But if those were much larger\Nnumbers this method might
Dialogue: 0,0:01:03.15,0:01:04.77,Default,,0000,0000,0000,,become a little difficult.
Dialogue: 0,0:01:04.77,0:01:08.52,Default,,0000,0000,0000,,So I'm going to show you using\Nexponent rules you can actually
Dialogue: 0,0:01:08.52,0:01:12.34,Default,,0000,0000,0000,,multiply exponentials or\Nexponent numbers without
Dialogue: 0,0:01:12.34,0:01:15.72,Default,,0000,0000,0000,,actually having to do as much\Narithmetic or actually you
Dialogue: 0,0:01:15.72,0:01:18.12,Default,,0000,0000,0000,,could handle numbers much\Nlarger than your normal math
Dialogue: 0,0:01:18.12,0:01:20.78,Default,,0000,0000,0000,,skills might allow you to.
Dialogue: 0,0:01:20.78,0:01:23.06,Default,,0000,0000,0000,,So let's just think what\N2 to the third times
Dialogue: 0,0:01:23.06,0:01:24.67,Default,,0000,0000,0000,,2 to the fifth means.
Dialogue: 0,0:01:24.67,0:01:32.94,Default,,0000,0000,0000,,2 to the third is 2\Ntimes 2 times 2, right?
Dialogue: 0,0:01:32.94,0:01:35.20,Default,,0000,0000,0000,,And we're multiplying that\Ntimes 2 to the fifth.
Dialogue: 0,0:01:35.20,0:01:43.16,Default,,0000,0000,0000,,And that's 2 times 2\Ntimes 2 times 2 times 2.
Dialogue: 0,0:01:43.16,0:01:44.20,Default,,0000,0000,0000,,So what do we have here?
Dialogue: 0,0:01:44.20,0:01:47.87,Default,,0000,0000,0000,,We have 2 times 2 times\N2, times 2 times 2 times
Dialogue: 0,0:01:47.87,0:01:49.78,Default,,0000,0000,0000,,2 times 2 times 2.
Dialogue: 0,0:01:49.78,0:01:52.64,Default,,0000,0000,0000,,Really all we're doing is we're\Nmultiplying 2 how many times?
Dialogue: 0,0:01:52.64,0:01:58.92,Default,,0000,0000,0000,,Well, one, two, three, four,\Nfive, six, seven, eight.
Dialogue: 0,0:01:58.92,0:02:03.41,Default,,0000,0000,0000,,So that's the same thing\Nas 2 to the eighth.
Dialogue: 0,0:02:03.41,0:02:05.05,Default,,0000,0000,0000,,Interesting.
Dialogue: 0,0:02:05.05,0:02:08.20,Default,,0000,0000,0000,,3 plus 5 is equal to 8.
Dialogue: 0,0:02:08.20,0:02:12.36,Default,,0000,0000,0000,,And that makes sense because 2\Nto the 3 is 2 multiplying by
Dialogue: 0,0:02:12.36,0:02:15.40,Default,,0000,0000,0000,,itself three times, to the\Nfifth is 2 multiplying by
Dialogue: 0,0:02:15.40,0:02:17.54,Default,,0000,0000,0000,,itself five times, and then\Nwe're multiplying the two, so
Dialogue: 0,0:02:17.54,0:02:19.98,Default,,0000,0000,0000,,we're going to multiply\N2 eight times.
Dialogue: 0,0:02:19.98,0:02:22.72,Default,,0000,0000,0000,,I hope I achieved my goal\Nof confusing you just now.
Dialogue: 0,0:02:22.72,0:02:23.58,Default,,0000,0000,0000,,Let's do another one.
Dialogue: 0,0:02:26.13,0:02:33.78,Default,,0000,0000,0000,,If I said 7 squared\Ntimes 7 to the fourth.
Dialogue: 0,0:02:33.78,0:02:36.55,Default,,0000,0000,0000,,That's a 4.
Dialogue: 0,0:02:36.55,0:02:42.18,Default,,0000,0000,0000,,Well, that equals 7 times 7,\Nright, that's 7 squared,
Dialogue: 0,0:02:42.18,0:02:44.43,Default,,0000,0000,0000,,times and now let's\Ndo 7 to the fourth.
Dialogue: 0,0:02:44.43,0:02:50.09,Default,,0000,0000,0000,,7 times 7 times 7 times 7.
Dialogue: 0,0:02:50.09,0:02:53.78,Default,,0000,0000,0000,,Well now we're multiplying\N7 by itself six times, so
Dialogue: 0,0:02:53.78,0:02:56.59,Default,,0000,0000,0000,,that equal 7 to the sixth.
Dialogue: 0,0:02:56.59,0:03:00.13,Default,,0000,0000,0000,,So in general, whenever I'm\Nmultiplying exponents of the
Dialogue: 0,0:03:00.13,0:03:04.62,Default,,0000,0000,0000,,same base, that's key, I can\Njust add the exponents.
Dialogue: 0,0:03:04.62,0:03:12.52,Default,,0000,0000,0000,,So 7 to the hundredth power\Ntimes 7 to the fiftieth
Dialogue: 0,0:03:12.52,0:03:15.44,Default,,0000,0000,0000,,power, and notice this\Nis an example now.
Dialogue: 0,0:03:15.44,0:03:17.75,Default,,0000,0000,0000,,It would be very hard without\Na computer to figure out what
Dialogue: 0,0:03:17.75,0:03:19.32,Default,,0000,0000,0000,,7 to the hundredth power is.
Dialogue: 0,0:03:19.32,0:03:22.19,Default,,0000,0000,0000,,And likewise, very hard without\Na computer to figure out what
Dialogue: 0,0:03:22.19,0:03:24.05,Default,,0000,0000,0000,,7 to the fiftieth power is.
Dialogue: 0,0:03:24.05,0:03:32.73,Default,,0000,0000,0000,,But we could say that this is\Nequal to 7 to the 100 plus 50,
Dialogue: 0,0:03:32.73,0:03:37.79,Default,,0000,0000,0000,,which is equal to 7 to the 150.
Dialogue: 0,0:03:37.79,0:03:40.43,Default,,0000,0000,0000,,Now I just want to give you a\Nlittle bit of warning, make
Dialogue: 0,0:03:40.43,0:03:41.63,Default,,0000,0000,0000,,sure that you're multiplying.
Dialogue: 0,0:03:41.63,0:03:49.15,Default,,0000,0000,0000,,Because if I had 7 to the 100\Nplus 7 to the 50, there's
Dialogue: 0,0:03:49.15,0:03:50.59,Default,,0000,0000,0000,,actually very little\NI could do here.
Dialogue: 0,0:03:50.59,0:03:54.44,Default,,0000,0000,0000,,I couldn't simplify\Nthis number.
Dialogue: 0,0:03:54.44,0:03:56.71,Default,,0000,0000,0000,,But I'll throw out one to you.
Dialogue: 0,0:03:56.71,0:04:04.81,Default,,0000,0000,0000,,If I had 2 to the 8 times\N2 to the 20, we know we
Dialogue: 0,0:04:04.81,0:04:06.57,Default,,0000,0000,0000,,can add these exponents.
Dialogue: 0,0:04:06.57,0:04:12.50,Default,,0000,0000,0000,,So that gives you 2\Nto the 28, right?
Dialogue: 0,0:04:12.50,0:04:20.82,Default,,0000,0000,0000,,What if I had 2 to the\N8 plus 2 to the 8?
Dialogue: 0,0:04:20.82,0:04:22.89,Default,,0000,0000,0000,,This is a bit of a\Ntrick question.
Dialogue: 0,0:04:22.89,0:04:25.03,Default,,0000,0000,0000,,Well I just said if\Nwe're adding, we can't
Dialogue: 0,0:04:25.03,0:04:26.90,Default,,0000,0000,0000,,really do anything.
Dialogue: 0,0:04:26.90,0:04:28.53,Default,,0000,0000,0000,,We can't really simplify it.
Dialogue: 0,0:04:28.53,0:04:30.67,Default,,0000,0000,0000,,But there's a little trick\Nhere that we actually have
Dialogue: 0,0:04:30.67,0:04:32.98,Default,,0000,0000,0000,,two 2 to the 8, right?
Dialogue: 0,0:04:32.98,0:04:35.08,Default,,0000,0000,0000,,There's 2 to the 8 times\N1, 2 to the 8 times 2.
Dialogue: 0,0:04:35.08,0:04:41.24,Default,,0000,0000,0000,,So this is the same thing as 2\Ntimes 2 to the 8, isn't it?
Dialogue: 0,0:04:41.24,0:04:42.15,Default,,0000,0000,0000,,2 times 2 to the 8.
Dialogue: 0,0:04:42.15,0:04:44.94,Default,,0000,0000,0000,,That's just 2 to\Nthe 8 plus itself.
Dialogue: 0,0:04:44.94,0:04:49.03,Default,,0000,0000,0000,,And 2 times to the 8, well\Nthat's the same thing as 2 to
Dialogue: 0,0:04:49.03,0:04:53.17,Default,,0000,0000,0000,,the first times 2 to the 8.
Dialogue: 0,0:04:53.17,0:04:55.50,Default,,0000,0000,0000,,And 2 to the first times 2 to\Nthe 8 by the same rule we just
Dialogue: 0,0:04:55.50,0:04:59.04,Default,,0000,0000,0000,,did is equal to 2 to the 9.
Dialogue: 0,0:04:59.04,0:05:01.08,Default,,0000,0000,0000,,So I thought I would just\Nthrow that out to you.
Dialogue: 0,0:05:01.08,0:05:03.28,Default,,0000,0000,0000,,And it works even with\Nnegative exponents.
Dialogue: 0,0:05:03.28,0:05:13.84,Default,,0000,0000,0000,,If I were to say 5 to the\Nnegative 100 times 3 to the,
Dialogue: 0,0:05:13.84,0:05:18.37,Default,,0000,0000,0000,,say, 100 -- oh sorry, times\N5 -- this has to be a 5.
Dialogue: 0,0:05:18.37,0:05:20.14,Default,,0000,0000,0000,,I don't know what my\Nbrain was doing.
Dialogue: 0,0:05:20.14,0:05:25.15,Default,,0000,0000,0000,,5 to the negative 100 times\N5 to the 102, that would
Dialogue: 0,0:05:25.15,0:05:27.89,Default,,0000,0000,0000,,equal 5 squared, right?
Dialogue: 0,0:05:27.89,0:05:30.93,Default,,0000,0000,0000,,I just take minus 100 plus 102.
Dialogue: 0,0:05:30.93,0:05:31.94,Default,,0000,0000,0000,,This is a 5.
Dialogue: 0,0:05:31.94,0:05:35.08,Default,,0000,0000,0000,,I'm sorry for that\Nbrain malfunction.
Dialogue: 0,0:05:35.08,0:05:37.86,Default,,0000,0000,0000,,And of course, that equals 25.
Dialogue: 0,0:05:37.86,0:05:39.21,Default,,0000,0000,0000,,So that's the first\Nexponent rule.
Dialogue: 0,0:05:39.21,0:05:40.76,Default,,0000,0000,0000,,Now I'm going to show you\Nanother one, and it kind of
Dialogue: 0,0:05:40.76,0:05:43.90,Default,,0000,0000,0000,,leads from the same thing.
Dialogue: 0,0:05:43.90,0:05:55.28,Default,,0000,0000,0000,,If I were to ask you what 2 to\Nthe 9 over 2 to the 10 equals,
Dialogue: 0,0:05:55.28,0:05:56.94,Default,,0000,0000,0000,,that looks like that could\Nbe a little confusing.
Dialogue: 0,0:05:56.94,0:06:00.72,Default,,0000,0000,0000,,But it actually turns out to be\Nthe same rule, because what's
Dialogue: 0,0:06:00.72,0:06:03.11,Default,,0000,0000,0000,,another way of writing this?
Dialogue: 0,0:06:03.11,0:06:08.36,Default,,0000,0000,0000,,Well, we know that this is also\Nthe same thing as 2 to the 9
Dialogue: 0,0:06:08.36,0:06:12.71,Default,,0000,0000,0000,,times 1 over 2 to\Nthe 10, right?
Dialogue: 0,0:06:12.71,0:06:14.46,Default,,0000,0000,0000,,And we know 1 over 2 to the 10.
Dialogue: 0,0:06:14.46,0:06:18.70,Default,,0000,0000,0000,,Well, you could re-write right\Nthis as 2 the 9 times 2 to
Dialogue: 0,0:06:18.70,0:06:20.85,Default,,0000,0000,0000,,the negative 10, right?
Dialogue: 0,0:06:20.85,0:06:25.27,Default,,0000,0000,0000,,All I did is I took 1 over 2 to\Nthe 10 and I flipped it and I
Dialogue: 0,0:06:25.27,0:06:26.99,Default,,0000,0000,0000,,made the exponent negative.
Dialogue: 0,0:06:26.99,0:06:28.33,Default,,0000,0000,0000,,And I think you know\Nthat already from
Dialogue: 0,0:06:28.33,0:06:30.66,Default,,0000,0000,0000,,level two exponents.
Dialogue: 0,0:06:30.66,0:06:33.09,Default,,0000,0000,0000,,And now, once again, we can\Njust add the exponents.
Dialogue: 0,0:06:33.09,0:06:39.30,Default,,0000,0000,0000,,9 plus negative 10 equals 2 to\Nthe negative 1, or we could
Dialogue: 0,0:06:39.30,0:06:42.00,Default,,0000,0000,0000,,say that equals 1/2, right?
Dialogue: 0,0:06:42.00,0:06:44.73,Default,,0000,0000,0000,,So it's an interesting\Nthing here.
Dialogue: 0,0:06:44.73,0:06:48.11,Default,,0000,0000,0000,,Whatever is the bottom\Nexponent, you could put it in
Dialogue: 0,0:06:48.11,0:06:50.80,Default,,0000,0000,0000,,the numerator like we did here,\Nbut turn it into a negative.
Dialogue: 0,0:06:50.80,0:06:53.76,Default,,0000,0000,0000,,So that leads us to the second\Nexponent rule, simplification
Dialogue: 0,0:06:53.76,0:06:59.86,Default,,0000,0000,0000,,is we could just say that this\Nequals 2 to the 9 minus 10,
Dialogue: 0,0:06:59.86,0:07:02.19,Default,,0000,0000,0000,,which equals 2 to\Nthe negative 1.
Dialogue: 0,0:07:02.19,0:07:05.16,Default,,0000,0000,0000,,Let's do another\Nproblem like that.
Dialogue: 0,0:07:05.16,0:07:16.40,Default,,0000,0000,0000,,If I said 10 to the 200 over\N10 to the 50, well that
Dialogue: 0,0:07:16.40,0:07:23.64,Default,,0000,0000,0000,,just equals 10 to the 200\Nminus 50, which is 150.
Dialogue: 0,0:07:23.64,0:07:30.87,Default,,0000,0000,0000,,Likewise, if I had 7 to the\Nfortieth power over 7 to
Dialogue: 0,0:07:30.87,0:07:35.94,Default,,0000,0000,0000,,the negative fifth power,\Nthis will equal 7 to the
Dialogue: 0,0:07:35.94,0:07:41.42,Default,,0000,0000,0000,,fortieth minus negative 5.
Dialogue: 0,0:07:41.42,0:07:46.23,Default,,0000,0000,0000,,So it equals 7 to\Nthe forty-fifth.
Dialogue: 0,0:07:46.23,0:07:48.31,Default,,0000,0000,0000,,Now I want you to think about\Nthat, does that make sense?
Dialogue: 0,0:07:48.31,0:07:54.48,Default,,0000,0000,0000,,Well, we could have re-written\Nthis equation as 7 to the
Dialogue: 0,0:07:54.48,0:07:59.18,Default,,0000,0000,0000,,fortieth times 7 to\Nthe fifth, right?
Dialogue: 0,0:07:59.18,0:08:02.81,Default,,0000,0000,0000,,We could have taken this 1 over\N7 to the negative 5 and turn it
Dialogue: 0,0:08:02.81,0:08:06.64,Default,,0000,0000,0000,,into 7 to the fifth, and that\Nwould also just be 7
Dialogue: 0,0:08:06.64,0:08:08.16,Default,,0000,0000,0000,,to the forty-five.
Dialogue: 0,0:08:08.16,0:08:10.81,Default,,0000,0000,0000,,So the second exponent rule I\Njust taught you actually is no
Dialogue: 0,0:08:10.81,0:08:12.39,Default,,0000,0000,0000,,different than that first one.
Dialogue: 0,0:08:12.39,0:08:14.81,Default,,0000,0000,0000,,If the exponent is in the\Ndenominator, and of course, it
Dialogue: 0,0:08:14.81,0:08:18.21,Default,,0000,0000,0000,,has to be the same base and\Nyou're dividing, you subtract
Dialogue: 0,0:08:18.21,0:08:20.57,Default,,0000,0000,0000,,it from the exponent\Nin the numerator.
Dialogue: 0,0:08:20.57,0:08:23.39,Default,,0000,0000,0000,,If they're both in the\Nnumerator, as in this case, 7
Dialogue: 0,0:08:23.39,0:08:26.58,Default,,0000,0000,0000,,to the fortieth times 7 to the\Nfifth -- actually there's no
Dialogue: 0,0:08:26.58,0:08:29.37,Default,,0000,0000,0000,,numerator, but they're\Nessentially multiplying by each
Dialogue: 0,0:08:29.37,0:08:32.42,Default,,0000,0000,0000,,other, and of course, you have\Nto have the same base.
Dialogue: 0,0:08:32.42,0:08:35.69,Default,,0000,0000,0000,,Then you add the exponents.
Dialogue: 0,0:08:35.69,0:08:37.70,Default,,0000,0000,0000,,I'm going to add one variation\Nof this, and actually this is
Dialogue: 0,0:08:37.70,0:08:40.36,Default,,0000,0000,0000,,the same thing but it's a\Nlittle bit of a trick question.
Dialogue: 0,0:08:40.36,0:08:56.47,Default,,0000,0000,0000,,What is 2 to the 9\Ntimes 4 to the 100?
Dialogue: 0,0:08:56.47,0:08:58.19,Default,,0000,0000,0000,,Actually, maybe I shouldn't\Nteach this to you, you have
Dialogue: 0,0:08:58.19,0:08:59.48,Default,,0000,0000,0000,,to wait until I teach\Nyou the next rule.
Dialogue: 0,0:08:59.48,0:09:01.90,Default,,0000,0000,0000,,But I'll give you\Na little hint.
Dialogue: 0,0:09:01.90,0:09:09.57,Default,,0000,0000,0000,,This is the same thing as 2 the\N9 times 2 squared to the 100.
Dialogue: 0,0:09:09.57,0:09:12.32,Default,,0000,0000,0000,,And the rule I'm going to teach\Nyou now is that when you have
Dialogue: 0,0:09:12.32,0:09:15.61,Default,,0000,0000,0000,,something to an exponent and\Nthen that number raised to
Dialogue: 0,0:09:15.61,0:09:18.93,Default,,0000,0000,0000,,an exponent, you actually\Nmultiply these two exponents.
Dialogue: 0,0:09:18.93,0:09:24.98,Default,,0000,0000,0000,,So this would be 2 the\N9 times 2 to the 200.
Dialogue: 0,0:09:24.98,0:09:27.02,Default,,0000,0000,0000,,And by that first rule\Nwe learned, this would
Dialogue: 0,0:09:27.02,0:09:29.76,Default,,0000,0000,0000,,be 2 to the 209.
Dialogue: 0,0:09:29.76,0:09:31.14,Default,,0000,0000,0000,,Now in the next module\NI'm going to cover
Dialogue: 0,0:09:31.14,0:09:31.94,Default,,0000,0000,0000,,this in more detail.
Dialogue: 0,0:09:31.94,0:09:34.65,Default,,0000,0000,0000,,I think I might have\Njust confused you.
Dialogue: 0,0:09:34.65,0:09:37.05,Default,,0000,0000,0000,,But watch the next video and\Nthen after the next video I
Dialogue: 0,0:09:37.05,0:09:40.40,Default,,0000,0000,0000,,think you're going to be ready\Nto do level one exponent rules.
Dialogue: 0,0:09:40.40,0:09:41.93,Default,,0000,0000,0000,,Have fun.