Amy, Lin, and Miguel were practicing creating equivalent expressions for (153)9

Question

. Amy got an expression of 1527
, Miguel got an expression of 1512
, and Lin got an expression of 153
. Who correctly used the Power Rule of Exponents to create an equivalent expression? (1 point)
Responses

Lin
Lin

Amy
Amy

Miguel
Miguel

Amy and Miguel

Answer 1

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

Here, we can simplify \( (15^3)^9 \) as follows:

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

Now, let's look at the expressions given by Amy, Lin, and Miguel:

• Amy has \( 15^{27} \), which is correctly calculated as \( 1527 \).
• Miguel has \( 15^{12} \), which is incorrect.
• Lin has \( 15^3 \), which is also incorrect.

Based on this analysis, the only correct expression is by Amy, who has provided \( 1527 \).

Therefore, the correct response is:

Amy