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Don't get all freaked out about these -- it's just a different notation for what you've already been doing.
 

cube root of 8can be written as 8^(1/3)
sqrt(15)can be written as 15^(1/2)

* Remember that the square root symbol is really the square root symbol with a little 2 on it ...  We just assume the 2.

Not that bad, is it?

Here's the general rule:

the nth root of a = a^(1/n)

This notation has some advantages because it will help you understand some things better.

Check it out:

sqrt(5) * sqrt(5) = ( 5^(1/2) ) * ( 5^(1/2) ) = 5^( 1/2 + 1/2 ) = 5^1 = 5

Now, we can show why this rule works:

( the nth root of a ) * ( the nth root of b ) = the nth root of ab

( the nth root of a ) * ( the nth root of b ) = ( a^(1/n) ) * ( b^(1/n) ) = ( ab )^(1/n) = the nth root of ab