Final answer:
To rewrite the expression using the fewest possible exponents, raise each term inside the parentheses to the power of 3, multiply the exponents of the remaining terms, and combine the expressions. The final expression is 8d^19f^10.
Step-by-step explanation:
To rewrite the expression using the fewest possible exponents, we can apply the exponent rules. First, we raise each term inside the parentheses to the power of 3:
(2d^5 f)^3 = (2^3)(d^(5*3))(f^3) = 8d^15f^3
Next, we multiply the exponents of the remaining terms:
(d^4 f^7) = d^4 * f^7 = d^4f^7
Finally, we combine the two expressions:
(8d^15f^3)(d^4f^7) = 8d^(15+4)f^(3+7) = 8d^19f^10