Unit 6 Indices and Factors

Unit 6Indices and Factors

Presentation 1 Square and Square Roots

Presentation 2 Cube and Cube Roots

Presentation 3 Index Notation

Presentation 4 Rules of Indices

Presentation 5 Factors

Presentation 6 Prime Factors

Presentation 7 HCF and LCM

Presentation 8 Negative Indices

Unit 6 Indices and Factors

Square and Square Roots

What is

We say that 4 is the square root of 16

So is also a square root of 16

We write

What is

What is the square root of 25?

as

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Square and Square Roots

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Cube and Cube Roots

What is

We say that the cube root of 125 is 5 and that

or

What is

Also


Cube and Cube Roots


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Index Notation

What is

What is

Find n if

So


Index Notation


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Rules of Indices

Verify rule for

(using rule)

But

(as before!)

m and n are integers

Verify rule for

But

(as before!)

Verify rule for

But

(as before!)


Rules of Indices


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Factors

A factor of a positive whole number is any positive whole number that will divide exactly into it.

Example: Find all the factors of 20

You can write 20 as:

So factors of 20 in increasing order are:

1 2 4 5 10 20


Factors


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Prime Factors

Any positive whole number can be written uniquely as the product of its prime factors.

Example: Write the number 276 as a product of its prime factor

This is unique

?

?

?


Prime Factors


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HCF and LCM

The HCF (Highest Common Factor) of two (or more) positive integers is the largest number which is a factor of both (or all) the numbers.

Example: Find the HCF of 120 and 105

So, HCF = 3 x 5 = 15

Check: ,

The LCM (Lowest Common Multiple) of two (or more) positive integers in the lowest number into which both (or all) of the numbers can divide exactly.

Example: Find the LCM of 24 and 60

Multiples of 24 are:

Multiples of 60 are:

So LCM = 120

Check ,

24, 48,72, 96,120, 144, . . .

60, 120, 180, 240, 300, . . .


HCF and LCM


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Presentation 6 Standard Form

Presentation 7 Calculations and Standard Form


Negative Indices

We define

Evaluate

Evaluate

Evaluate

Evaluate


Negative Indices


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Unit 6 Indices and Factors