To simplify the expression \( 7^{15} \) using the Power Rule of Exponents, we should express it in a way that reveals its expanded form.
The Power Rule states that \( (a^m)^n = a^{m \cdot n} \).
Let's analyze the options:
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\( (7^{18})^3 \): This simplifies to \( 7^{18 \cdot 3} = 7^{54} \), which is not equivalent to \( 7^{15} \).
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\( (7 \cdot 7 \cdot 7 \cdot 7 \cdot 7)^{10} \): This equals \( (7^5)^{10} = 7^{5 \cdot 10} = 7^{50} \), which is not equivalent to \( 7^{15} \).
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\( (7^{10})^5 \): This simplifies to \( 7^{10 \cdot 5} = 7^{50} \), which is not equivalent to \( 7^{15} \).
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\( (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \): This represents \( 5 \) groups of \( (7 \cdot 7 \cdot 7) = 7^3 \). Hence, this expands to \( (7^3)^5 = 7^{3 \cdot 5} = 7^{15} \), which is equivalent to \( 7^{15} \).
Therefore, the correct answer is:
(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7).