To identify which expression correctly uses the power rule of exponents, let's briefly review the power rule. The power rule states that \( (a^m)^n = a^{m \cdot n} \).
Now, let's evaluate each expression:
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\((7^4)^8\):
- This can be expressed using the power rule: \[ (7^4)^8 = 7^{4 \cdot 8} = 7^{32} \]
- This is a correct application of the power rule.
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\((-5)^0\):
- Any non-zero number raised to the power of 0 is 1, which is not directly an application of the power rule but rather a property of exponents.
- This doesn't utilize the power rule.
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\((7^8) \cdot (7^{10})\):
- This can be combined using the property of exponents: \[ 7^8 \cdot 7^{10} = 7^{8+10} = 7^{18} \]
- This expression makes use of the property of exponents but does not specifically utilize the power rule.
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\(12^9\):
- This expression is simply in exponential form and does not employ any exponent rules.
Based on this analysis, the expression \((7^4)^8\) is the one that is correctly developed to use the power rule of exponents.