Part 2/6:
One of the first properties we can explore is the rule that defines ( x^0 ). By definition, any non-zero number raised to the power of zero equals one. This means ( 2^0 = 1), ( 5^0 = 1), and so forth. However, ( 0^0 ) is a more complex discussion that warrants further exploration in future discussions.
Multiplication of Powers
Another essential property of power functions is that when you multiply two powers with the same base, you can add their exponents. For example, ( x^a \cdot x^b = x^{a+b} ).
To illustrate, if you have ( x^2 \cdot x^3 ), this equates to ( x^{2+3} = x^5 ). This property arises from the very definition of exponents.