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.

Memory text

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 $2^(10-4)\=2^6$

$2^6=2\times2\times2\times2\times2\times2$

$2^6=64$