Final answer:
The expression (-125)^1/3 in radical notation is written as the cube root of -125, which can be denoted as √[-125] with a small 3 to the left of the radical symbol indicating the cubic root.
Step-by-step explanation:
To use radical notation to write the expression (-125)^1/3, we are effectively looking for the cube root of -125. Radical notation indicates the use of a radical symbol to denote roots, and the cube root is represented with an index of 3 in the radical. Thus, the expression (-125)^1/3 can be written in radical notation as √[-125]. Here √ signifies the radical symbol with an invisible index of 2, which stands for square root, and for cube root, we would place a small 3 to the left of the radical symbol to indicate the cube root.
In mathematics, a negative exponent such as x^-n indeed represents the reciprocal of x^n, that is 1/x^n. However, in this question, we are dealing with a fractional exponent which denotes roots. For example, x^(1/2) refers to the square root of x, and likewise, x^(1/3) refers to the cube root of x. Applying this principle, (-125)^(1/3) is the cube root of -125.