If the expression 715

Question

was simplified, which of the following would be an expanded equivalent expression?(1 point)
Responses

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

(718)3
open paren 7 to the 18th power close paren cubed

7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7
7 times 7 times 7 times 7 times 7 times 7 times 7 times 7 times 7 times 7 times 7 times 7 times 7 times 7 times 7

(710)5

Answer 1

To simplify the expression \(715\), we note that it is equivalent to \(7^{15}\).

Now, we need to find an expanded equivalent expression among the options provided:

1. (7⋅7⋅7⋅7⋅7)10: This is equal to \(7^{5 \times 10} = 7^{50}\). This is not equivalent to \(7^{15}\).

2. (718)3: This is equal to \( (7^{18})^3 = 7^{54}\). This is not equivalent to \(7^{15}\).

3. 7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7: This expression consists of 15 sevens multiplied together, which is exactly \(7^{15}\). This is equivalent to \(715\).

4. (710)5: This is equal to \( (7^{10})^5 = 7^{50}\). This is not equivalent to \(7^{15}\).

Therefore, the correct answer is:

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