Raising a positive proper fraction to a natural number __________________ has a result that is less than that fraction a. Sometimes b. Always c. Never

Question

Raising a positive proper fraction to a natural number __________________ has a result that is less than that fraction a. Sometimes b. Always c. Never

Answer 1

Here is an intuitive way to look at it:  Each time you take a fraction of a fraction, you are left with less of less.

Answer 2

Under the stated conditions, a power such as 2 or 3 or more of a proper fraction > 0 has the effect of yielding a result that is ALWAYS LESS than the original fraction.  You can experiment with various numbers to assure yourself that this is so--this will be quite instructive.