So 64 can be written as
Keep this in mind.
So by the definition of roots,
Now substituting the prime factorization of 64 in place of 64, and writing it as an exponent as previously shown we get,
Using the law for the power of a power, we multiply the exponents together which gives us,
Also what is (n^3m^9)^1/2?
Using the same law of exponents the outside exponent gets "distributed" to each inside term.
Or we can also do it this way,
These are all equivalent statements.