To simplify the expression \( 2x^5 \cdot 12x^{-4} \), the correct exponent rules to apply would be the product of powers rule and then also multiply the coefficients.
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Product of Powers Rule: This rule states that when multiplying two expressions with the same base, you add the exponents. In this case: \[ x^5 \cdot x^{-4} = x^{5 + (-4)} = x^{1} \]
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Coefficients: You also multiply the numerical coefficients: \[ 2 \cdot 12 = 24 \]
Putting it together, you would have: \[ 2x^5 \cdot 12x^{-4} = 24x^{1} \]
So the correct response would be: "The product exponent rule to add \(5 + (-4)\) to get an exponent of \(1\) on the \(x\). You would also multiply \(2 \cdot 12\) since they are coefficients."