Suppose we have a fraction that is raised to such and such a negative fractional exponent. For example, suppose we have 16/81^-1/3. What do we do in such a case? First, we invert the fraction so that it reads 81/16, and then we turn the fractional exponent -1/3 to its positive counterpart, 1/3. Now, when we say that we are looking for 30/4^1/3, all this means is that we are looking for the cubed root of 81/16. We deal with the cubed roots of the numerator and the denominator separately. The cubed root of 16 is 4 and the cubed root of 81 is 27. Therefore, the answer is 27/4.
March 22, 2014