Suppose we have a problem like 4^1/4. Those who are relatively new to exponents may be confused. Yet we can easily solve this problem. We simply put the denominator to the top left of the square root sign, such that it is clear that the problem is asking for the 4th root of the number 4. The denominator is placed to the upper left of the square root sign, and the base is eplaced under the square root sign, as we have already seen. Keep in mind that, strictly speaking, the expression 4^1/4 is a meaningless expression. It has no answer because 4 has no 4th root. It does, however, have a square root. Thte square root is expressed by 4^1/2. The reason for this, keep in mind, is that when we ordinarily see a number under a square root symbol, the implied number to the top left of the square root symbol is 2. This is asking for the "2nd" root, or the square root.
March 25, 2014