# AQA Mathematics Core 2 - Indicies

Powerful stuff...

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• Created by: Aline
• Created on: 01-04-10 21:28

## Basic rules

Make sure you know these rules- they are the shizzle!!

• x^a X x^b = x^ a+b (when multiplying powers, add the indices)
• x^a / x^b = x^a-b (when dividing powers, subtract the indices)
• (x^a)^b = x^ab (when finding powers of powers, multiply the indices)
• x^0 = 1 (any number to the power of 0 is ALWAYS 1)
• x^ -a = x^ (1/x^a) ( turn a negative power into a fraction)
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## Examples..

Write 9^5 as a power of 3.

9= 3^2

9^5= (3^2)^5

2X5 = 10

9^5 = 3^10

Write (1/4)^5 as a power of 2.

1/4= 1/2^2 = 2^ -2

(2^ -2)^5 = 2^(-2 X 5)

=2^ -10

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## Roots a hoy!

This won't have any symbols in because unfortunately my keyboard doesn't have a root sign. Sorry!

More Rules to learn...

• the nth root.. when n is even, it stands for a POSITIVE nth root)
• x^(1/n) = the nth root of x
• x^(m/n) = (x^1/n)^m = (nth root of x)^m OR nth root of (x^m)
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## Examples...

Evaluate 36^(1/2)

squared root of 36 = 6

Write (x X squared root of x) ^ 3 as a power of x

squared root of x = x^(1/2)

(x X x^(1/2) ) ^3 = x^3 X x^(3/2)

=x^(9/2)

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