Amy, Lin, and Miguel were practicing creating equivalent expressions 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

Miguel
Miguel

Amy
Amy

Amy and Miguel
Amy and Miguel
Remaining Attempts : 3
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Answer 1

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

In this case:

• Base \(a\) is \(15\),
• \(m\) is \(3\),
• \(n\) is \(9\).

So, we calculate: \[ (15^3)^9 = 15^{3 \cdot 9} = 15^{27}. \]

Now let's analyze the responses:

• Amy got \(15^{27}\), which is correct.
• Miguel got \(15^{12}\), which is incorrect since \(3 \cdot 9\) does not equal \(12\).
• Lin got \(15^3\), which is also incorrect since it does not represent the simplification of the original expression.

Thus, the only correct response is Amy.

Correct answer: Amy