The Power Rule of Exponents states that \((a^m)^n = a^{m \cdot n}\).
In this case, we can apply this rule to \((15^3)^9\):
\[ (15^3)^9 = 15^{3 \cdot 9} = 15^{27} \]
Now, let's analyze the results from each person:
- Amy got \(15^{27}\), which is correct.
- Miguel got \(15^{12}\), which is incorrect because he might have mistakenly calculated \(3 + 9\) instead of multiplying.
- Lin got \(15^{3}\), which is incorrect because that doesn't apply the power rule at all.
Therefore, the only correct equivalent expression is Amy's.
The correct answer is: Amy.