The Power Rule of Exponents states that \((a^m)^n = a^{m \cdot n}\). To identify which of the provided expressions is correctly developed to use this rule, let's analyze each one:
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\((7^8) \times (7^{10})\) - This expression does not use the Power Rule but rather the Product of Powers Rule, which states \(a^m \times a^n = a^{m+n}\).
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\((-5)^0\) - According to the Zero Exponent Rule, any non-zero base raised to the power of 0 equals 1, but it doesn't illustrate the use of the Power Rule.
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\((7^4)^8\) - This expression uses the Power Rule of Exponents, and can be calculated as \(7^{4 \cdot 8} = 7^{32}\).
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\(12^9\) - This is just a single power expression and does not illustrate the use of the Power Rule.
The correct expression that illustrates the Power Rule of Exponents is:
\((7^4)^8\)