Final answer:
To simplify the given expression, we divide the exponents and combine like terms to get y^(-41/4).
Step-by-step explanation:
To simplify the expression, we can apply the rules of exponents. First, let's simplify the numerator: (y⁴)⁻³/⁴ can be written as (y⁴)⁻³ x (y⁴)⁻¹/⁴. Using the rule that (aⁿ)ⁱ = aⁿⁱ, this becomes y⁻¹² x y⁻¹/⁴. Next, let's simplify the denominator: (y¹/⁴)⁵ can be written as y⁵/⁴. Now, we can combine the numerator and denominator by dividing the exponents: y⁻¹² x y⁻¹/⁴ ÷ y⁵/⁴. Using the rule that a⁻ⁿ = 1/aⁿ, this simplifies to 1/y¹² x y⁻¹/⁴ x y⁻⁵/⁴. Finally, we can simplify this expression further by combining the like terms: y⁻¹² x y⁻¹/⁴ x y⁻⁵/⁴ = y^(-12-1/4-5/4). Simplifying the exponent, we have y^(-41/4).