Final answer:
The expression suggested by the student, after simplification, equals 10900√6y¹¹, which doesn't match any of the provided choices. Thus, it's likely that the original question is incorrect or has been miscommunicated.
Step-by-step explanation:
The student is asking to simplify the following algebraic expression: 2725y⁸ * 4√6y³, under the condition that y > 0. Let's solve this step by step:
- First, recognize that 4√6 can be written as 4 * 6¹⁄₄, which equals 4 * √6 because taking a fourth root is the same as raising to the power of 1/4.
- Now we combine the constant terms 2725 and 4, and the y terms y⁸ and y³.
- To multiply the constants, calculate: 2725 * 4 = 10900.
- To multiply the y terms with exponents, we add the exponents: y⁸ * y³ = y⁻¹₁ since 8 + 3 = 11.
- Now multiply by √6, resulting in: 10900y¹¹ * √6.
- Since there's no option matching this form, it means that the original options were incorrect, or there was an error in interpreting the question. We cannot match it to any of the provided choices.
In conclusion, the expression 2725y⁸ * 4√6y³ simplifies to 10900√6y¹¹, but none of the provided options match this result.