If the expression 7^15

Question

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

(7^10)^5
open paren 7 to the 10th power close paren to the 5th power

(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)
open paren 7 times 7 times 7 close paren times open paren 7 times 7 times 7 close paren times open paren 7 times 7 times 7 close paren times open paren 7 times 7 times 7 close paren times open paren 7 times 7 times 7 close paren

(7⋅7⋅7⋅7⋅7)^10
open paren 7 times 7 times 7 times 7 times 7 close paren to the 10th power

(7^18)^3

Answer 1

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

We can break down \( 7^{15} \) as follows:

1. (7^10)^5: \[ (7^{10})^5 = 7^{10 \cdot 5} = 7^{50} \] This is not equivalent to \( 7^{15} \).

2. (7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7): This represents 5 groups of \( 7^3 \): \[ (7^3)^5 = 7^{3 \times 5} = 7^{15} \] This is equivalent to \( 7^{15} \).

3. (7⋅7⋅7⋅7⋅7)^10: This represents \( 7^5 \) raised to the 10th power: \[ (7^5)^{10} = 7^{5 \cdot 10} = 7^{50} \] This is not equivalent to \( 7^{15} \).

4. (7^18)^3: \[ (7^{18})^3 = 7^{18 \cdot 3} = 7^{54} \] This is also not equivalent to \( 7^{15} \).

Thus, the only equivalent expression to \( 7^{15} \) from the options provided is:

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