00:00Hi everybody, so in this
00:02lesson we're going to look
00:02at the laws of exponents.
00:03Here they are. Note these
00:05are not in the formula
00:06booklet, so we need to
00:08know them. Now I'm going
00:09to go straight into the
00:10examples and we refer to
00:13each, I think each of
00:14these laws will be used
00:17in these examples. So the
00:18first one is, base are
00:20the same, base is are
00:21the same, we just add
00:22the exponents. So this becomes
00:23m to the power of
00:2410, 7 plus 3 is
00:2510. Base is are the
00:27same and we're dividing.
00:28This becomes p to power
00:293. As I subtract the
00:31exponents. The reason for that
00:32is because p to the
00:33power of 5 is p
00:34times p times p times
00:37p times p and p
00:38squared is p times p.
00:41And then two of these
00:42cancel with two of these.
00:43So you're left with 5
00:44minus 2 which is 3.
00:46Okay, big ugly looking complicated
00:49thing in the bracket to
00:50the power of 0. Answer
00:51is 1. Anything to the
00:54power of 0 is 1.
00:55How nice is that?
00:56Now if the zero is
00:57just with the y, be
00:59careful then it would just
01:00be the y would become
01:011 and you'd be left
01:02with the 60 square root
01:03of a 14. Okay, 2
01:05to the negative 3 equals,
01:07so this is a rule
01:08that comes up often and
01:10causes problems. If you have
01:12a negative power, that's the
01:13same as 1 over 2
01:16to the positive power, which
01:18is actually 1 over 8.
01:20And the reason for that
01:21is, imagine we had
01:24Imagine I had 2 to
01:27the power of 3 divided
01:30by 2 to the power
01:33of 7. Well this is
01:372 times 2 times 2
01:39over 2 times 2 times
01:412 times 2 times 2
01:44times 2. So let's do
01:47the power of 3 over
01:482 to the power of
01:487. And what happens is
01:50this cancels with this, this
01:51cancels with this,
01:52this cancel with this, this
01:53cancels with this, and we're
01:54left with 1 over 2
01:57to the power of 4.
01:59But we know the rule,
02:01this rule says 3 minus
02:047 has to be negative
02:064. So this has to
02:07be 2 to the negative
02:084, and this has to
02:10be 1 over 2 to
02:11the power 4. So that's
02:12why a negative power brings
02:15it underneath the line like
02:16so. Okay, this one mixes
02:18those first two. So 2,
02:20basically,
02:20These are the same. I'm
02:21going to add the powers
02:21for the numerator is 12
02:23and it's 2 to the
02:25power of 8. And then
02:26I'll do it separately. I
02:28could have written 1, go,
02:2912 minus 8 is 4,
02:31but here I'll do 12
02:31minus 8 is 4, 2
02:33to the power of 4,
02:34which is 16. Okay, this
02:37one, 3 squared times 5
02:40squared. So this time the
02:41power is the same. It's
02:42this rule here. The powers
02:43are the same and I'm
02:44going backwards. So I can
02:45multiply the bases.
02:48and keep the power as
02:502, so 15 squared, which
02:51is 225. Last question, x
02:56to the zero is 1,
02:57so I can ignore that.
02:58x squared cubed, that's this
03:00one. x squared cubed, outside
03:03the brackets, I multiply the
03:05power, so 2 times 3
03:06is 6. Let's guess x
03:08squared cubed is x squared,
03:10times x squared, times x
03:12squared. 2 plus 2 plus
03:132 is 6.
03:16I divide x squared times
03:18x to the minus six
03:20will be x to the
03:21negative four. And then it's
03:26six minus negative four, which
03:28would actually be x to
03:30the power of 10. Okay,
03:34so obviously a range of
03:35difficulty there in the questions
03:36I did. I went through
03:37quite quickly. Hopefully we know
03:43most of these rules.
03:44only one I think they
03:45didn't do is this rule,
03:46but this works the exact
03:47same as the multiplication rule.
03:49If you're dividing and the
03:51powers are the same, you
03:52just divide the bases and
03:54keep the power. Yeah, hopefully
03:57we know how to do
03:58all that or we knew
03:59how to do it before.
04:01If not, go practice some
04:02questions.