how do you find the lenght of a segment with given exponents?

To find the length of a segment with given exponents, you need to clarify what you mean by "given exponents." If you are referring to a segment with two endpoints given as coordinate points in a coordinate system, you can calculate its length using the distance formula. The distance formula is derived from the Pythagorean theorem and is applicable in two or three dimensions.

The distance formula in two-dimensional space (x, y) is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) and (x2, y2) represent the coordinates of the two endpoints of the segment, and d represents the length of the segment.

If you are working in three-dimensional space (x, y, z), the distance formula is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)

Again, (x1, y1, z1) and (x2, y2, z2) represent the coordinates of the endpoints, and d represents the length of the segment.

Please note that if you are referring to exponents in a different context, such as algebraic equations or exponential functions, you will need to provide more specific details about the problem or equation you're working with for further clarification.