[ Video Instruction: Rational Exponents ]
Assume all variables are positive and use the rules of exponents to simplify.
Notice that all of the above problems worked out nicely because the exponents were multiples of the root. This is not always the case as illustrated below.
A quick way to simplify radicals is to divide the index into the exponents. This will tell us what the exponent of the base should be outside the radical and the remainder will be the exponent of the base inside the radical. All the rules of exponents hold true when working with rational exponents.
J. Redden on G+