Final answer:
The equivalent expression for (64xy⁴) ¹⁄² is A) 8xy² because the square root of 64 is 8, x remains the same, and y⁴ becomes y² when taking the square root.
Step-by-step explanation:
To find the equivalent expression for (64xy⁴) ¹⁄², we need to take the square root of each factor inside the parentheses. The square root of 64 is 8, and taking the square root of x is just x since it's already to the first power. The square root of y⁴ (y to the fourth power) is y² (y to the second power), because we divide the exponent by 2 when taking a square root.
Accordingly, the expression (64xy⁴) ¹⁄² simplifies to 8xy². Therefore, the correct answer is A) 8xy².