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.