Monomials and Indices Slideshow 7, Mathematics Room 307, Mr. Sasaki
Feb 22, 2016
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