Zero Exponent and Negative Integral Exponent A zero exponent indicates that the exponential function is undefined for that specific value. This means...
A zero exponent indicates that the exponential function is undefined for that specific value. This means that the function cannot be evaluated for any real value of x when x = 0.
For example, 2^0 is undefined, as it would be impossible to find the value of 2 raised to the power of 0.
On the other hand, a negative integral exponent indicates that the exponential function is defined for that specific value. This means that the function can be evaluated for all real values of x when x is positive.
For example, 2^(-1) = 1/2, as 2 raised to the power of -1 is equal to 1/2.
Important Points:
A zero exponent is always equal to 0.
A negative integral exponent can be positive or negative.
The exponential function is always continuous, except at x = 0 and x = infinity.
A zero exponent corresponds to a vertical asymptote, while a negative integral exponent corresponds to a horizontal asymptote