If the expression 715

Question

7
15
was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?(1 point)
Responses

(710)5
(
7
10
)
5
left parenthesis 7 superscript 10 baseline right parenthesis superscript 5 baseline

(7⋅7⋅7⋅7⋅7)10
(
7
⋅
7
⋅
7
⋅
7
⋅
7
)
10
left parenthesis 7 times 7 times 7 times 7 times 7 right parenthesis superscript 10 baseline

(718)3
(
7
18
)
3
left parenthesis 7 superscript 18 baseline right parenthesis cubed

(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)

Answer 1

To simplify the expression \( 7^{15} \), we apply the Power Rule of Exponents, which states that \( (a^m)^n = a^{m \cdot n} \).

If we consider \( 7^{15} \) and look for an equivalent expanded expression, we can express it in a way that reflects the multiplication of its factors. The expanded expression would need to show \( 7 \) multiplied by itself a total of 15 times.

Among the options provided, we are looking for an expression that represents \( 7^{15} \) correctly. Let's evaluate the given choices:

1. Option 1: \((7^{10})^5\) - This simplifies to \( 7^{10 \cdot 5} = 7^{50} \), which is not equal to \( 7^{15} \).

2. Option 2: \((7 \cdot 7 \cdot 7 \cdot 7 \cdot 7)^{10}\) - This indicates multiplying \( 7 \) five times and raising it to the power of 10, resulting in \( 7^{5 \cdot 10} = 7^{50} \), which is incorrect.

3. Option 3: \((7^{18})^3\) - This simplifies to \( 7^{18 \cdot 3} = 7^{54} \), still not equal to \( 7^{15} \).

4. Option 4: \((7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7)\) - Each parenthesis has 3 factors of \( 7 \) and there are 5 such groupings, leading to \( 7^{3 \cdot 5} = 7^{15} \).

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

The fourth option: \((7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7)\).