IB · Mathematics Applications & Interpretation (AI)
AISL 1.5.1 Laws of exponents
Learn AISL 1.5.1 Laws of exponents in this free IB Mathematics Applications & Interpretation (AI) video lesson for SL 1.5—Exponents and Logarithms.
Learn AISL 1.5.1 Laws of exponents in this free IB Mathematics Applications & Interpretation (AI) video lesson for SL 1.5—Exponents and Logarithms.
Learn AISL 1.5.1 Laws of exponents in this free IB Mathematics Applications & Interpretation (AI) video lesson for SL 1.5—Exponents and Logarithms.
The video lesson covers the laws of exponents, emphasizing their importance as they are not included in the formula booklet. Key concepts include:
The lesson also illustrates how to handle various exponent scenarios, including multiplying and dividing bases with the same exponent, and emphasizes the importance of practicing these rules for mastery.
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
00:21
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.