# AS Maths Core One Indices

These revision cards sum up all the rules you need to know on Indices for AS Maths Core 1.

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• Created by: naomi
• Created on: 12-11-09 20:18

When multiplying numbers with powers you can add the powers together.

eg. X^a x X^b = X^a+b

But only when the base numbers are the same.

eg. X^a x Y^b X Not Possible to add the powers here

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Simplify the following....

2^7 x 2^7 = 2^14

3^6 x 3^7 = 3^13

5^6 x 7^6= Cannot add the powers here because the base numbers are not the same.

a^8 x a^6 = a^14

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## Subtracting Powers

When dividing numbers with powers you can subtract the powers.

eg. X^a ÷ X^b = X^a-b

But only when the base numbers are the same.

eg. X^a x Y^b X Not Possible

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## Subtracting Powers

Simplify the following...

36 ÷ 3^2 = 3^4

5^5 ÷5^6= 5-1

t^8 ÷ t^4= t^4

n^3 ÷ m^5= Cannot subtract the powers here because the base numbers are different

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## Power on Power

When numbers with powers are in a bracket and there's a power outside the bracket too, you canmultiply the powers.

eg. (Xa)^b= Xaxb

When there's a term in the bracket in front of the Xyou must multiply that by the indice outside the bracket too.

eg. (2x^a)^b= 2^b x X^axb

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## Power on Power

Simplify the following...

(a4)^5 = a^20

(t-3)4= t-12

(3X^5)^4 = 81X^20

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## Write in the form 2^n

4^3 = 2 ^6

This is because 4^3 can also be written as (2^2)^3 because 2^2 is the same as 2 x 2 =4.

Therefore (2^2)^3 = 2^6 because you can multiply the powers.

eg. 8^2 = (2^3)^2 = 2^6

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## Write in the form 2^n

More complex example...

162 x 83 ÷ 322

Firstly you can write 16^2 as (2^4)^2

Then 8^3 as (2^3)^3

And 32^2 as (2^5)^2

So far we have (2^4)^2 x (2^3)^3 ÷ (2^5)2

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## Write in the form 2^n Continued

Using the power on power rule we can simplify this to:

2^8 x 2^9 ÷ 2^10

We can then use the adding power rule to simplify 2^8 x 2^9 =2^17

So 2^17 ÷ 2^10

Then we use the subtracting powers rule to get 2^7

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## Negative Powers

Negative powers indicate that the number can be written as a fraction for example

x-1 could be written as 1/x

or

x-2 could be written as 1/x2

or

x-3 could be written as 1/x^3

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## Negative powers

Write the following as fractions...

23 = 1/23 = 1/8

5-1 = 1/5

10-4 = 1/10^4 = 1/10000

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## Fractional Indices

When a number is to a fractional power there is an alternative way you can write it for example:

x^1/2 = x The square root of x to the power of one

or

x^1/3 = 3x The cube root of x to the power of one

The denominator determines what root it is and the numerator determines what power the base number is to.

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## Fractional Indices

Solve the following

9^1/2 = 9 = 3

27^1/3 = 327 = 3

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