April 13, 2023

Powers and indices

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April 13, 2023

The words “powers” and “indices” mean the same thing.

Look at this calculation… 2 × 2 The answer to this is 4.It is the same as writing

Look at this calculation…2 × 2 × 2 The answer to this is 8.It is the same as writing

Notice how the number of 2s there are is represented by the little number in 2² and 2³.

How might you also write 2 × 2 × 2 × 2 × 2 × 2? 2⁶

This is a form of shorthand, called powers, or indices.

2 squared, or 2²

2 cubed, or 2³

.

.

Explanation

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April 13, 2023

×

Indices can be used in combination with each other.

4× 74 74 7×× ×³ ³

5× 35 35 ×× ×³ ²

×8× p8 p8 p×× ×⁴ ³×8

Indices can also be used in combination with other mathematical functions.

×2× 72 72 7+× ×³ ³ +

Remember, you can only group numbers or letters that are the same and that are multiplied by each other.

×n× nn nn n+× ×³ ³

Explanation

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April 13, 2023Exercises

CLASSWORK:Page 209Exercise 8.1AAll questions.

EXTENSION:Page 210Exercise 8.1BAll questions.

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April 13, 2023

Instead of finding what the value of a letter in a formula is, you may be given the value of a letter to start with and be asked to find the value of the whole formula.

A statement such as 2x + 2 is a formula.

It is not an equation, because it does not show two equivalent statements, either side of an “=” sign.

Find the value of 2x + 2 when x = 2

2x + 2 = 2 × 2 + 2

= 6

Explanation

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April 13, 2023

Indices in the formula only apply to the previous number, or digit.

6n² means 6 × n × n not 6n × 6n

6n ²( ) means 6n × 6n

You can use brackets to keep your workings out clear.

5n² + 4Find the value of when n = 3

5n² + 4 = (3 ²)5 + 4

= 5 × 9 + 4= 49

Explanation

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April 13, 2023

=

The numbers substituted into formula may be positive, negative, decimals or fractions.Remember that the square of a negative number is a positive number.

A negative number to the power of any odd number gives a negative answer.

²-6This is the same for all even indices.

= 36

³-6 -216

3p² + 4Find the value of when p = -3

3p² + 4 = (-3 ²)3 + 4

= 3 × 9 + 4= 31

Explanation

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