Question

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

(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)
left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis

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

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

(7 superscript 18) superscript 3

Answer 1

To simplify \(7^{15}\) using the Power Rule of Exponents, we recognize that \(7^{15}\) means multiplying the base \(7\) by itself \(15\) times. The equivalent expanded expression will thus be showing \(7\) multiplied by itself \(15\) times.

Among the provided options, the expression that correctly represents this is:

\[
(7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7)
\]

This expression demonstrates \(5\) groups of \(3\) \(7\)s multiplied, which totals \(15\) \(7\)s when counted.

Therefore, the correct response is:

\[
(7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7)
\]