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