Final answer:
The simplified expression with only positive exponents is ⅓y¹¹/x.
Step-by-step explanation:
To simplify the expression 2y⁵x⁻⁴/6x⁻³y⁻⁸ using only positive exponents, we will follow the rules for dividing powers with the same base. First, divide the coefficients (2/6) to get ⅓. Next, subtract the exponents for x, which means adding the negative exponents (-4 - (-3) = -4 + 3 = -1). This gives us x⁻¹. Similarly, subtract the exponents for y (5 - (-8) = 5 + 8 = 13) resulting in y¹¹. To express the answer with positive exponents, we flip the base with a negative exponent to the denominator, resulting in ⅓y¹¹/x.