It represents the ratio between the numerator and the denominator. It is totally misleading to suggest that it represent anything like "parts of a whole". The ratio of the surface area of a sphere to its volume is 3/r. In this expression 3 parts out of the "total" radius is not a particularly meaningful or useful concept.
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In a fraction, the numerator represent the part out of the denominator which represents the total. Neither need be rational (or even real).
It represents the order of the root that needs to be calculated. A denominator of 2 means a square root. A denominator of 3 means a cube root. And so on.
How do you use an exponent to represent a number such as 16
process by which a fraction containing radicals in the denominator is rewritten to have only rational numbers in the denominator.
A rational expression is not defined whenever the denominator of the expression equals zero. These will be the roots or zeros of the denominator.