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

Amy
Amy

Amy and Miguel
Amy and Miguel

Lin
Lin

Miguel

Answer 1

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

In this case: \[ (15^3)^9 = 15^{3 \cdot 9} = 15^{27} \]

Now let's evaluate the expressions provided by each person:

• Amy: \(15^{27}\) (correct)
• Miguel: \(15^{12}\) (incorrect, should be \(15^{27}\))
• Lin: \(15^{3}\) (incorrect, should be \(15^{27}\))

Therefore, Amy is the only one who correctly used the Power Rule of Exponents. The correct answer is:

Amy