Final answer:
To find an exponential expression equivalent to the given one, we can express it in terms of the natural exponential function e^(ln(b)), where b is the base of the original expression. This method also aligns with the principles of exponential growth, squaring, and cubing of exponentials.
Step-by-step explanation:
An exponential expression equivalent to the given one can be determined by understanding the rules of exponential arithmetic. Particularly, when casting a base to a power, we can use the exponential function with base e (approximately equal to 2.7183), since the natural logarithm functions as its inverse. Hence, if we have a base b, it can be expressed as e^(ln(b)).
For example, the number 2 can be written as e^(ln(2)). When combined with exponential growth, where a value doubles over time intervals, this transforms into the expression 2^n being equivalent to e^(n*ln(2)), where n is the number of doubling times.
By understanding squaring and cubing of exponentials, where the digit term is squared or cubed and the exponent is multiplied by 2 or 3 respectively, we can apply these principles to simplify or modify exponential expressions in various mathematical operations.