[HidyBush]

I mean, this is true for every operation once you extend it to a new domain.

What is exponentiation? is 5^6 multiplying 5 for 6 times? sure, but how about 5^(-6)? what's up with that? and 5^(1/2)? and don't get me started on 5^(2/3)

[vikingerik]

Those follow. 5^(1/2) is multiplying by 5 one-halfth of a time. It is half the operation of multiplying by 5. Applying that operation twice results in 5.

5^(2/3) is two-thirds of the operation of multiplying by 5. Applying that operation three times results in multiplying by 5 for six-thirds times, or twice, and the result is 25.

5^-6 is multiplying by 5 negative-six times. What is multiplying a negative number of times? Dividing. You divide by 5 six times.