Final answer:
The expression (x^5y)/(x^2y^4) simplifies to x^3 / y^3 by subtracting the exponents for like bases and moving any terms with negative exponents to the denominator to ensure all exponents are positive.
Step-by-step explanation:
To simplify the expression (x^5y)/(x^2y^4), we need to apply the rules of division of exponentials. The rule states that you can subtract the exponents when dividing like bases. For the variables with exponents, we subtract the exponent of the denominator from the exponent of the numerator. So, for the variable x, we have x^5 / x^2 which simplifies to x^(5-2) or x^3. For the variable y, we have y / y^4 which simplifies to y^(1-4) or y^(-3). However, since the problem asks for positive exponents only, we can rewrite y^(-3) as 1 / y^3 by moving it to the denominator.
Putting this all together, the simplified expression with only positive exponents is x^3 / y^3.