Indices law - law 3
`a^(1/n)=\rootna`
To remember this try simple numbers you know first.
We know `4^(1/2)=sqrt4=2`
We can then apply this to all other examples:
Example 1
`10\^(1/2)=\root2\10=3.162`
Example 2
`9\^(1/2)=\root2\9=3` `(3xx3 =9)`
The second root of `9=3`
(The second root is also known as the square root)
Example 3
`27\^(1/3)=\root3\27=3` `(3xx3xx3=27)`
The third root of `27=3`
(The third root is also known as the cube root)
Example 4
`8\^(2/3)`
| Because | `1/2xx1/2=1/4` |
| then | `2/3=1/3xx2/1` |
| or | `1/3xx2` |
`8\^(2/3)=8\^(1/3xx2)`
Law 5 states `a\^(mn)=(a\^(m))\^(n)`
`8\^(2/3)=8\^(1/3xx2)=(8\^(1/3))\^(2)=(\root3\8)\^(2)`
`(8\^(1/3))\^(2)=(\root3\8)\^(2)=2\^(2)=4`
