Final answer:
The expression 28p⁹q⁻⁵/12p⁻⁶q⁷ is equivalent to 7p¹⁵q¹²/3.
Step-by-step explanation:
To simplify the expression 28p⁹q⁻⁵/12p⁻⁶q⁷, we can apply the quotient rule of exponents. According to the rule, when dividing two terms with the same base, we subtract the exponents. So, in this case, the p terms will simplify to p^(9-(-6)) = p^15, and the q terms will simplify to q^(-5-7) = q^-12. Therefore, the simplified expression is 28p^15q^-12/12. Now, we can divide the numerator and denominator by the common factor of 4, resulting in 7p^15q^-12/3. Therefore, the expression is equivalent to option D: 7p¹⁵q¹²/3.