Final answer:
The expression '$3' does not translate to a standard mathematical exponential form, and if it's a typo, none of the provided options (a, b, c, d) correctly express the number 3 in exponential form. 3 in exponential form is simply 3^1. Cubing of exponentials involves cubing the base number and multiplying the exponent by 3, but this does not apply to the number 3 alone.
Step-by-step explanation:
To convert the expression $3 to exponential form, we need to clarify what the $ symbol represents. Usually, in mathematics, the dollar sign is not used as a mathematical operation or function. Assuming that there is a typo and the intention is to express the number 3 in one of the exponential forms provided - (a) 31/4, (b) 43, (c) 41/3, or (d) 43 - none of these options correctly express the number 3 in exponential form. The number 3 in exponential form is simply 31, as any number raised to the power of 1 is itself.
When dealing with the cubing of exponentials, you would cube the base number and multiply the exponent by 3. For example, (22)3 = 22*3 = 26. However, this is not applicable here as 3 is not being cubed, and the exponent is not given as a variable to multiply.
If the question was to express the cube of 3 in exponential form, it would be written as 33, but this is not one of the provided options.