To determine which of the given options is an expanded equivalent expression for \( 7^{15} \) using the Power Rule of Exponents, we need to break down the expression \( 7^{15} \) into a form that clearly shows multiplication of the base (7) a total of 15 times.
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The expression \((7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7) \cdot (7 \cdot 7 \cdot 7)\) has 5 groups of 3 sevens each (which equals 15). So, this simplifies to \( 7^{15} \).
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The expression \((7^{18})^3\) would equal \( 7^{54} \), which is not equivalent to \( 7^{15} \).
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The expression \((7^{10})^5\) would equal \( 7^{50} \), which is not equivalent to \( 7^{15} \).
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The expression \((7 \cdot 7 \cdot 7 \cdot 7 \cdot 7)^{10}\) has 5 sevens multiplied together, which equals \( 7^5 \). When raised to the power of 10, that becomes \( 7^{50} \), which is not equivalent to \( 7^{15} \).
Considering the above options, the correct answer is:
(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)