Summary Indices laws to remember

`3` laws to remember are:

A positive is multiply   `a^n\=(a)(a) ... ... . (a)`  .......................... Law 1

A negative is divide   `a^-n\=1/a^n`   .................................................. Law 2

A fraction is root   `a^(1/n)=rootna`  ........................................................... Law 3       

The following you should be able to work out by trying simple numbers you know first. 

`a^0=1`

`a^ma^n=a^(m+n)`

`a^mdiva^n=(a^m)/(a^n)=a^(m-n)`

`(a^m)^n=a^(mn)`

`(ab)^n=a^nb^n`

`(a/b)^n=((a^n)/(b^n))`

Simple examples include:

`10^0=1`

`10^2=10\times10`

`10^-2=1/10^2=1/(10\times10)`

So then we can tackle examples as:

`8^0.666=8^(2/3)=(root3\8)^2=(2)^2=4`

And finally therefore

`8^(2/3)`  means what do we have to multiply by itself `3` times to get `8` and then multiply the answer by itself `2` times.