Changing Exponents to Radicals:

How to convert radicals within exponential form has been explained.   Sometimes therefore, it is essential or convenient to convert exponents to radicals.  Recognizing in which an exponent is the equivalent of the nth root is meaningful to help comprehend an expression.

The expression 5^1/3 could be written as 3√5.  It is algebraically expressed as:

a^1/m = ^m√a

The above definition can be more commonly described as:

ⁿ√a^m = (a^m)^1/n = a ^m/n

and

(ⁿ√b)^m = (b^1/n)^m = b^m/n

Examples: 15 ^2/3 = ³√15²

16 ^½ = ²√16 =4