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Monomials and Indices. Slideshow 7, Mathematics Room 307 , Mr. Sasaki. Objectives. Recall previously learnt properties of indices Understand how to calculate numbers in the form a -x and . Apply these new rules to simplifying monomials. Recalling Properties of Indices. - PowerPoint PPT Presentation
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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 =รท =4 ๐ฅ2x =6 ๐ฅ4รท =5
Here are some of the rules for indices that you have learned so far.Letโs 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? Letโs look a little closer.
=๐ฆร ๐ฆ๐ฆร ๐ฆร๐ฆ=1๐ฆ
So by doing this we can see thatโฆ
Other Properties of Indices
๐ฆ โ1=1๐ฆ And this would continueโฆ
-2 =1๐ฆ 2-7 =1๐ฆ 7
- =1๐ฆ ๐ฅ
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!
โ161612= =ยฑ 4 (Donโt worry about
negative roots.)
Other Properties of IndicesHow about ? For this, we find the cube root.
12513=3โ125=5
How about a horrible oneโฆ243
15=5โ243=3
Soโฆ๐ฅ1๐ฆ=๐ฆโ๐ฅ
Other Properties of IndicesSo now we have a lot to play with!Letโs try some examplesโฆExamples๐ถ๐๐๐๐ข๐๐๐ก๐ 16
32 .16
32=43=64
.
๐ถ๐๐๐๐ข๐๐๐ก๐ 81โ 12 .81
โ 12=9โ1=19
It doesnโt matter which part of the calculation you do first, do whichever is easiest!
Try the worksheet!
Answers
64 36 4 64 ๐๐๐
๐๐
๐๐
๐๐๐
๐๐๐
๐๐๐
๐๐๐
๐๐๐
๐๐๐
๐๐๐๐
4 27 2253 10
118 1
4 2432
4932 64 ยผ
ยฝ
Other Properties of IndicesSo hopefully you rememberโฆ
๐ฅ๐๐ฅ๐ร ยฟ๐ฅ๐+๐
And now you may have found thatโฆ)b ยฟ๐ฅ๐๐ร
So be careful, these are very different.
Monomials and IndicesLetโs try applying this to some monomials.ExamplesWrite 32๐ฅโ 2๐๐ ๐ ๐๐๐๐๐ก๐๐๐ .32๐ฅโ 2=9 ๐ฅโ2=
9๐ฅ2
โ
Write(16ยฟยฟ12๐ฆ )
โ2
๐๐ ๐ ๐๐๐๐๐ก๐๐๐ .ยฟ
(16ยฟยฟ12๐ฆ )
โ 2
ยฟ=(4 ๐ฆ )โ 2=1
16 ๐ฆ2
Try the last worksheet!
Answers
or 10
1023 22
25 35
82+ 4ยฝ or
7๐2
149๐2
64๐2
14096 ๐2
18๐2๐2
๐22๐
1
8 ๐ฅ32
๐16
Answers โ 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 โ Monomials Review1๐
1๐ฅ3
2๐ฆ4
๐ฅ212 ๐ฆ
164๐3
4๐12 2๐ 2๐
12
2 ๐ฅ13 3 ๐ฅ ๐ฅ
14
1
๐ฅ12
4
๐ฆ12
1
3 ๐ง12
1
9๐12
1
3๐13
1
4 ๐ฅ14
4
4๐32 8 ๐
32
27 ๐ฅ34
243 ๐ฅ8 ๐ฅ23 8 ๐ฅ
32
8
๐23
1
27๐32
1
64๐34
๐ฅ32
12519๐
1
3๐ฅ13