Final answer:
The given expression ((x^7y^6)/(x^2y))^4 is simplified by subtracting exponents for the same base within the parentheses, resulting in (x^5y^5)^4. After applying the rule of multiplying exponents when raised to a power, the final simplified answer with positive exponents is x^20y^20.
Step-by-step explanation:
To simplify the expression ((x^7y^6)/(x^2y))^4, we first apply the Division of Exponentials rule which states that when dividing exponential terms with the same base, we subtract the exponents of those terms. Thus, for the term x we have x^7/x^2 = x^(7-2) = x^5, and for the term y we have y^6/y = y^(6-1) = y^5. After simplifying inside the parentheses, the expression becomes (x^5y^5)^4.
Next, we follow the rule that states when raising an exponent to a power, we multiply the exponents. This gives us (x^5)^4 * (y^5)^4, which simplifies to x^(5*4) * y^(5*4) = x^20 * y^20. Therefore, the simplified expression with only positive exponents is x^20y^20.