Final answer:
The expression (x^1/4/y^5/6)^12 simplifies to x^3/y^10 by raising both numerator and denominator to the 12th power separately.
Step-by-step explanation:
To simplify the expression (x1/4 / y5/6)12, we need to apply the exponent to both the numerator and the denominator separately, which is an example of the Division of Exponentials. By multiplying the exponents, we get:
- x1/4 raised to the 12th power is x(1/4)*12 or x3.
- y5/6 raised to the 12th power is y(5/6)*12 or y10.
Therefore, the simplified expression is x3 / y10.