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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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