To simplify the expression \( 7^{15} \) using the Power Rule of Exponents, we can break it down using the properties of exponents. The Power Rule states that \( (a^m)^n = a^{m \cdot n} \).
Looking at the provided options, the equivalent expressions can be analyzed as follows:
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(7⋅7⋅7⋅7⋅7)^{10}: This equals \( (7^5)^{10} = 7^{50} \), which is not equivalent to \( 7^{15} \).
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(7^{18})^3: This equals \( 7^{54} \), which is also not equivalent to \( 7^{15} \).
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(7^{10})^5: This equals \( 7^{50} \), which again is not equivalent to \( 7^{15} \).
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(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7): This expression has 5 groups of \( 7 \cdot 7 \cdot 7 \) (which is equal to \( 7^3 \)), so we can write it as \( (7^3)^5 = 7^{15} \).
Based on this analysis, the option that is an expanded equivalent expression of \( 7^{15} \) is:
(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7).