To apply the power rule of exponents correctly, we need to understand the conditions under which the rule can be applied. The power rule states that \((a^m)^n = a^{m \cdot n}\) and \(a^m \cdot a^n = a^{m+n}\).
Let's analyze each expression:
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\(12^9\):
- This expression is already in its simplest form. It doesn't involve applying the power rule.
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\((-5)^0\):
- According to the zero exponent rule, any non-zero base raised to the power of 0 is equal to 1. This doesn't involve the power rule but rather the zero exponent rule.
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\((7^8) \cdot (7^{10})\):
- This expression can be simplified using the product of powers rule. According to this rule: \((7^8) \cdot (7^{10}) = 7^{8 + 10} = 7^{18}\).
- This is a correct application of exponent rules.
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\((7^4)^8\):
- This expression can be simplified using the power of a power rule. According to this rule: \((7^4)^8 = 7^{4 \cdot 8} = 7^{32}\).
- This is also a correct application of the power rule of exponents.
So, the expressions that correctly use the power rule are:
- \((7^8) \cdot (7^{10})\) which simplifies to \(7^{18}\), and
- \((7^4)^8\) which simplifies to \(7^{32}\).
Both of these expressions correctly utilize the power rule of exponents.
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