There are three rules to remember - known as the Laws of Indices.
They only apply when working with the same base numbers.
The laws deal with raising base numbers to powers.
For example:
`2^3 xx 2^4`
`= (2xx2xx2) xx (2xx2xx2xx2) = 2^7`
which is the same as adding the indices.
The law for multiplying is `2^m xx 2^n = 2^((m+n))`
There is a similar law for dividing:
`4^5 ÷ 4^3`
`= frac(4xx4xx4xx4xx4)(4xx4xx4)`
`= 4 xx4 = 4^2`
and in this case the same answer is obtained by subtracting the indices.
The law for dividing: `4^m÷4^n=4^((m-n))`
When raising a number to a further power, the indices are multiplied:
`(5^3)^2` (5 raised to the power of three, then raised to the power of 2)
`(5 xx5 xx 5) xx (5 xx 5 xx 5) = 5^6`
and can be re-written by multiplying the indices.
The law for raised to a power: `(5^m)^n = 5^((mxxn))`.
Calculate 93 x 34. Give your answer as a power of 3.
93 x 34
9 can be changed to 32, so that the base numbers are the same
= (32)3 x 34
= 3(3x2 + 4)
= 310
Answer: 310
What is 45 ÷ 45?
`4^5 ÷ 4^5`
`= frac(4xx4xx4xx4xx4)(4xx4xx4xx4xx4)`
`= frac(1)(1) = 1 = 4^0`. Anything raised to the power of zero is always 1.
Answer: 1
See also Terms with Powers