Significant figures is a way of trying to convey how accurately something is being measured. A very accurate scale may measure .001 grams, a bathroom scale may be only accurate to within 2 lbs.
Exponential notation has nothing to do with measurement. It is just a choice on how to write a number, usually for some mathematical application. 243 = 35 this is exponential 'notation'. Scientific notation is a certain type of exponential notation in which the base must be 10. 243 = 2.43 x 102 that is scientific notation.
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Exponent=e to the powerPower=m to the power ni.e Power=Generalized exponent
In terms of mathematical concepts, there is no difference at all. In practical terms, some rational exponents or rational number will result in rational answers while radical exponent won't. But that is hardly a significant difference.
You can but it has no particular significance.
In their simplest forms, a base number is the number that is being multiplied by itself while the exponent is the number of times that the base is multiplied.