Part 4/6:
Extended calculations reveal intriguing results:
For ( 3^{1/10} ), the value approaches ( 1.116 ).
For ( 3^{1/100} ), it further refines to approximately ( 1.01 ).
This systematic approach of using a calculator to iterate through various fractions of 3 demonstrates the persistent trend towards one, emphasizing the continuous nature of power functions.
The Enigma of Zero to the Zero
Shifting focus to ( 0^0 ), we find that:
For any positive exponent, ( 0^x = 0 ).
For negative exponents, ( 0^{-x} ) leads to an undefined condition stemming from division by zero.