Final answer:
The radical expression that correctly represents 2 times d to the power of seven tenths is '2 times the tenth root of d to the power of 7', which corresponds to Option 3.
Step-by-step explanation:
The radical expression that represents 2 times d to the power of seven tenths can be expressed in the form of a radical and an exponent. To write the expression 2d7/10, you need to understand that the numerator of the fraction exponent indicates the power, and the denominator indicates the root. Therefore, the expression 7/10 implies the seventh power and the tenth root.
The correct option must reflect this relationship between exponents and roots. Among the provided options, Option 3: 2 times the tenth root of d to the power of 7 is equivalent to 2d7/10. This is because taking the tenth root of d7 is the same as raising d to the power of 7/10, and since the 2 is outside the radical, it is multiplied by the result of the root. Hence, Option 3 correctly represents the expression 2 times d to the power of seven tenths.