Monomials and IndicesSlideshow 7, Mathematics
Room 307, Mr. Sasaki
Recall previously learnt properties of indices
Understand how to calculate numbers in the form a-x and .
Apply these new rules to simplifying monomials.
Objectives
Simplify the following:
Recalling Properties of Indices
x =Γ· =4 π₯2x =6 π₯4Γ· =5
Here are some of the rules for indices that you have learned so far.Letβs look at a few more!
We know how to calculate with indices, but what do they mean?
Other Properties of Indices
ExampleCalculate .
=Well, we knew that. Is there anything else? Letβs look a little closer.
=π¦Γ π¦π¦Γ π¦Γπ¦=1π¦
So by doing this we can see thatβ¦
Other Properties of Indices
π¦ β1=1π¦ And this would continueβ¦
-2 =1π¦ 2-7 =1π¦ 7
- =1π¦ π₯
How about ? Other Properties of Indices
Well if means to square , would mean to do the opposite. ( means inverse.)What is the opposite of squaring something?Square rooting something!
β161612= =Β± 4 (Donβt worry about
negative roots.)
Other Properties of IndicesHow about ? For this, we find the cube root.
12513=3β125=5
How about a horrible oneβ¦243
15=5β243=3
Soβ¦π₯1π¦=π¦βπ₯
Other Properties of IndicesSo now we have a lot to play with!Letβs try some examplesβ¦ExamplesπΆππππ’πππ‘π 16
32 .16
32=43=64
.
πΆππππ’πππ‘π 81β 12 .81
β 12=9β1=19
It doesnβt matter which part of the calculation you do first, do whichever is easiest!
Try the worksheet!
Answers
64 36 4 64 πππ
ππ
ππ
πππ
πππ
πππ
πππ
πππ
πππ
ππππ
4 27 2253 10
118 1
4 2432
4932 64 ΒΌ
Β½
Other Properties of IndicesSo hopefully you rememberβ¦
π₯ππ₯πΓ ΒΏπ₯π+π
And now you may have found thatβ¦)b ΒΏπ₯ππΓ
So be careful, these are very different.
Monomials and IndicesLetβs try applying this to some monomials.ExamplesWrite 32π₯β 2ππ π πππππ‘πππ .32π₯β 2=9 π₯β2=
9π₯2
β
Write(16ΒΏΒΏ12π¦ )
β2
ππ π πππππ‘πππ .ΒΏ
(16ΒΏΒΏ12π¦ )
β 2
ΒΏ=(4 π¦ )β 2=1
16 π¦2
Try the last worksheet!
Answers
or 10
1023 22
25 35
82+ 4Β½ or
7π2
149π2
64π2
14096 π2
18π2π2
π22π
1
8 π₯32
π16
Answers β Numbers Review
14
11219
136
1125
1128
2 3 34 3 414
110
110
151615
14 216 6258 49 641918
1243
13125
132
11296
Answers β Monomials Review1π
1π₯3
2π¦4
π₯212 π¦
164π3
4π12 2π 2π
12
2 π₯13 3 π₯ π₯
14
1
π₯12
4
π¦12
1
3 π§12
1
9π12
1
3π13
1
4 π₯14
4
4π32 8 π
32
27 π₯34
243 π₯8 π₯23 8 π₯
32
8
π23
1
27π32
1
64π34
π₯32
12519π
1
3π₯13