Question

If the expression 7^15 was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?(1 point) Responses (7^18)^3
(7^10)^5
(7⋅7⋅7⋅7⋅7)^10
(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)

Answer 1

To simplify \( 7^{15} \) using the Power Rule of Exponents, we can express \( 7^{15} \) in different equivalent forms. The Power Rule states that \( (a^m)^n = a^{m \cdot n} \).

Let's evaluate each option:

1. **\( (7^{18})^3 \)**
- This would equal \( 7^{18 \cdot 3} = 7^{54} \), which is not equivalent to \( 7^{15} \).

2. **\( (7^{10})^5 \)**
- This would equal \( 7^{10 \cdot 5} = 7^{50} \), which is also not equivalent to \( 7^{15} \).

3. **\( (7 \cdot 7 \cdot 7 \cdot 7 \cdot 7)^{10} \)**
- This is equal to \( 7^5 \) raised to the 10th power:
- \( (7^5)^{10} = 7^{5 \cdot 10} = 7^{50} \), which again is not equivalent to \( 7^{15} \).

4. **\( (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \)**
- This represents \( 5 \) groups of \( 3 \) twos:
- That results in \( 7^{3 \cdot 5} = 7^{15} \), which **is equivalent** to \( 7^{15} \).

Thus, the correct answer, which represents an expanded equivalent expression for \( 7^{15} \), is:

**\( (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \)**.