To determine which expression is correctly developed to use the Power Rule of Exponents, we can review the options provided:
- \( 8 (7^4)^8 \)
- \( 12^9 \)
- \( (-5)^0 \)
- \( (78) \cdot (7^{10}) \)
The Power Rule of Exponents states that \((a^m)^n = a^{m \cdot n}\), so we are looking for an expression where this rule is applicable.
Analysis:
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\( 8 (7^4)^8 \): This expression correctly applies the Power Rule when simplifying \( (7^4)^8 \). It can be simplified to \( 8 \cdot 7^{32} \) because \( 4 \cdot 8 = 32 \).
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\( 12^9 \): This is a single base raised to an exponent and does not involve the Power Rule.
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\( (-5)^0 \): According to the exponent rules, any non-zero number raised to the power of 0 equals 1. This does not utilize the Power Rule.
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\( (78) \cdot (7^{10}) \): This is a multiplication of two separate expressions, and does not utilize the Power Rule.
Conclusion: The correct expression that is developed to use the Power Rule of Exponents is \( 8 (7^4)^8 \), as it applies the Power Rule when simplifying \( (7^4)^8 \) to \( 7^{32} \).