Question

why do whole numbers raised to an exponent get greater while fractions raised to an exponent get smaller?

Answer 1

Because 3^2 = 9
When you do (⅓)^2 what you are really doing is
(1^2)/(3^2) = 1/9


If you have (⅔)^2 you do
(2^2)/(3^2) = 4/9

Fractions get smaller because the denominator is also being squared which makes the denominator get bigger and when the denominator is bigger, you are dividing by a larger number which gives you a smaller answer. Whereas when you raise a whole number to an exponent, only the numerator get bigger because the denominator is 1 and 1 raised to any exponent is still 1

3^2 = (3^2)/(1^2) = 9/1 = 9