Simplify each expression using the product rule if possible.
$(-4{)}^6(-4)$

• A. $\left(-4\right)^5$
• B. $4^7$
• C. $\left(-4\right)^7$
• D. $\left(-4\right)^8$

Answer: (C)

Verified step by step guidance

1. Recall the Product Rule for Exponents: when multiplying two expressions with the same base, you add the exponents. This rule is written as \(a^{m} \times a^{n} = a^{m+n}\).
2. Identify the base and the exponents in the given problem. Make sure the bases are the same before applying the Product Rule.
3. Apply the Product Rule by adding the exponents together while keeping the base the same. For example, if you have \(x^{3} \times x^{5}\), you write it as \(x^{3+5}\).
4. Simplify the exponent addition to get the new exponent. Using the previous example, \(x^{3+5}\) becomes \(x^{8}\).
5. Write the final expression with the simplified exponent, ensuring the base remains unchanged and the exponents are combined correctly.