# 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.