To simplify the expression \( 715 \) using the Power Rule of Exponents, we can first rewrite \( 715 \) in terms of base \( 7 \).
This involves recognizing that \( 715 = 7^{15} \).
Now, if we were to apply the Power Rule of Exponents, it states that \( (a^m)^n = a^{m \cdot n} \). So, if we consider \( (7^{15})^1 \), we could also express this as \( 7^{15} \).
From the options provided, we look for an expanded form of \( 715 \) or \( 7^{15} \).
Here’s a breakdown of the given options:
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(718)³: This does not relate to \( 7^{15} \).
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(7ⁱ)³: This format does not match \( 7^{15} \).
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(7ⁱ)⁵: This could correspond if we had \( 15 = 5 \cdot 3 \), but it doesn’t equal \( 15 \) directly.
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(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7): This option represents \( 7^3 \) multiplied by itself 5 times, which gives \( 7^{3 \cdot 5} = 7^{15} \).
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(7⋅7⋅7⋅7⋅7)^{10}: This represents \( 7^5 \) raised to the 10th power, giving \( 7^{5 \cdot 10} = 7^{50} \).
The correct choice that expands to the equivalent of \( 7^{15} \) is:
(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)
2 answers