Amy, Lin, and Miguel were practicing creating equivalent expression for (15^3)^9.

Question

Amy got an expression of 15^27,
Miguel got an expression of 15^12,
and Lin got an expression of 15^3.
Who correctly used the Power Rule of Exponents to create an equivalent expression?(1 point)
Responses

Lin
Lin

Amy and Miguel
Amy and Miguel

Miguel
Miguel

Amy
Amy

Answer 1

To determine who correctly used the Power Rule of Exponents to simplify the expression \((15^3)^9\), we can apply the Power Rule, which states that \((a^m)^n = a^{m \cdot n}\).

In this case, we have:

\[ (15^3)^9 = 15^{3 \cdot 9} = 15^{27} \]

Now let's evaluate the responses:

• Amy got \(15^{27}\), which is correct.
• Miguel got \(15^{12}\), which is incorrect because he likely calculated \(3 \cdot 4\) instead of \(3 \cdot 9\).
• Lin got \(15^{3}\), which is also incorrect because that doesn’t follow the Power Rule.

Therefore, the only correct response is:

Amy.