The Power Rule of Exponents states that \((a^m)^n = a^{m \cdot n}\). We can apply this rule to the expression \((7^4)^8\).
Let's break down each option:
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\(12^9\): This expression is already in its simplest form and does not require the Power Rule of Exponents.
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\((7^4)^8\): This expression can be evaluated using the Power Rule: \[ (7^4)^8 = 7^{4 \cdot 8} = 7^{32} \] Thus, this is correctly developed using the Power Rule.
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\((-5)^0\): According to the property of exponents, any non-zero number raised to the power of 0 equals 1. Hence, this expression does not involve the Power Rule.
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\((7^8) \cdot (7^{10})\): This expression can be simplified using the rule \(a^m \cdot a^n = a^{m+n}\), but it is not an application of the Power Rule of Exponents.
Therefore, the correct expression that uses the Power Rule of Exponents is \((7^4)^8\).
5 answers