Final answer:
To find the value of 'y', raise the power to a power (5m^7)^3, resulting in 125m^21; therefore, 'y' equals 21 (option C).
Step-by-step explanation:
The student's question asks for the value of 'y' in the expression (5m^7)^3 = 125m^y. To solve this, we first need to recognize that when raising a power to a power, you multiply the exponents. The given expression can be expanded to 5^3 × m^(7×3), which simplifies to 125m^21. Therefore, comparing the simplified expression to 125m^y, we can see that the exponent 'y' must be 21. So the value of 'y' in the expression (5m^7)^3 = 125m^y is 21, which corresponds to option C.