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 `2^2\div2^3`

We know this equals `(2\times2)/(2\times2\times2)=1/2=0.5`

`1/2=2^-1` 

So, does `a^m\diva^n=a^m/a^n` ?

`2^2 divide 2^3 = (2^2)/(2^3)`

`4 divide 8 = 4/8` 

Yes it does.

And does `a^m\diva^n=a^(m-n)` ?

`2^2\div2^3=2^(2-3)=2^-1` 

`4 divide 8 = 1/2` 

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`