Monomials and Indices
description
Transcript of Monomials and Indices
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 =÷ =4 𝑥2x =6 𝑥4÷ =5
Here are some of the rules for indices that you have learned so far.Let’s 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? Let’s look a little closer.
=𝑦× 𝑦𝑦× 𝑦×𝑦=1𝑦
So by doing this we can see that…
Other Properties of Indices
𝑦 −1=1𝑦 And this would continue…
-2 =1𝑦 2-7 =1𝑦 7
- =1𝑦 𝑥
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!
√161612= =± 4 (Don’t worry about
negative roots.)
Other Properties of IndicesHow about ? For this, we find the cube root.
12513=3√125=5
How about a horrible one…243
15=5√243=3
So…𝑥1𝑦=𝑦√𝑥
Other Properties of IndicesSo now we have a lot to play with!Let’s try some examples…Examples𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 16
32 .16
32=43=64
.
𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 81− 12 .81
− 12=9−1=19
It doesn’t matter which part of the calculation you do first, do whichever is easiest!
Try the worksheet!
Answers
64 36 4 64 𝟏𝟐𝟕
𝟏𝟗
𝟏𝟒
𝟏𝟒𝟗
𝟏𝟏𝟐
𝟏𝟏𝟔
𝟏𝟖𝟏
𝟏𝟒𝟗
𝟏𝟖𝟏
𝟏𝟐𝟓𝟔
4 27 2253 10
118 1
4 2432
4932 64 ¼
½
Other Properties of IndicesSo hopefully you remember…
𝑥𝑎𝑥𝑏× ¿𝑥𝑎+𝑏
And now you may have found that…)b ¿𝑥𝑎𝑏×
So be careful, these are very different.
Monomials and IndicesLet’s try applying this to some monomials.ExamplesWrite 32𝑥− 2𝑎𝑠𝑎 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 .32𝑥− 2=9 𝑥−2=
9𝑥2
❑
Write(16¿¿12𝑦 )
−2
𝑎𝑠𝑎 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 .¿
(16¿¿12𝑦 )
− 2
¿=(4 𝑦 )− 2=1
16 𝑦2
Try the last worksheet!
Answers
or 10
1023 22
25 35
82+ 4½ or
7𝑎2
149𝑎2
64𝑎2
14096 𝑎2
18𝑎2𝑏2
𝑐22𝑎
1
8 𝑥32
𝑎16
Answers – 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 – Monomials Review1𝑎
1𝑥3
2𝑦4
𝑥212 𝑦
164𝑎3
4𝑎12 2𝑏 2𝑐
12
2 𝑥13 3 𝑥 𝑥
14
1
𝑥12
4
𝑦12
1
3 𝑧12
1
9𝑎12
1
3𝑎13
1
4 𝑥14
4
4𝑎32 8 𝑎
32
27 𝑥34
243 𝑥8 𝑥23 8 𝑥
32
8
𝑎23
1
27𝑎32
1
64𝑎34
𝑥32
12519𝑎
1
3𝑥13