Indices law - law 7 - Dividing powers = Subtract the powers
`a^m\diva^n=a^m/a^n=a^(m-n)`
To remember this: try simple numbers you know first
Try `10^2\div10^3`
We know this equals `(10\times10)/(10\times10\times10)=1/10=0.1`
`1/10=10^-1`
So, does `a^m\diva^n=a^m/a^n` ?
`10^2\div10^3=10^2/10^3=1/10=10^-1`
Yes it does.
And does `a^m\diva^n=a^(m-n)` ?
`10^2\div10^3=10^(2-3)=10^-1`
Yes it does
If you see a complicated index always try simple numbers first and then the difficult ones are easy.
Example
1. What is `x^6\divx^3` ?
It is either `(x\timesx\timesx\timesx\timesx\timesx)/(x\timesx\timesx)`
Which is `(x\timesx\timesx\timescancelx\timescancelx\timescancelx)/(cancelx\timescancelx\timescancelx)`
Which is `x^3`
OR
`x^6\divx^3`
Is `x^(6-3)=x^3`
2. What is `2^10\div2^4` ?
It is `2^(10-4)\=2^6`
`2^6=2\times2\times2\times2\times2\times2`
`2^6=64`
