Final answer:
The correct simplification of the expression (5xy⁵)²(y³)⁴ is 25x²y²², which is option A.
Step-by-step explanation:
To simplify the expression (5xy⁵)²(y³)⁴, we need to apply the laws of exponents. First, for the term (5xy⁵)², we raise both the coefficient (5) and the variables (x and y⁵) to the power of 2.
For the coefficient, 5 squared is 25. For the variables, x to the power of 2 is x² and y⁵ to the power of 2 is yµ² (which is y²² when the exponents are multiplied).
Secondly, for (y³)⁴, we raise y³ to the power of 4, which results in y³⁴ (or y²² when again, the exponents are multiplied).
Combining these results, we get 25x²y²² × y²². Finally, when variables with the same base are multiplied, we add their exponents together, so y²² × y²² becomes y´´. Thus, the fully simplified expression is 25x²y²², which matches option A.