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

• A. ${(-4)}^5$
• B. $4^7$
• C. ${(-4)}^7$
• D. ${(-4)}^8$

Answer: (C)

Verified step by step guidance

1. Recall the Product Rule for Exponents, which states that when multiplying two expressions with the same base, you add their exponents: \(a^{m} \times a^{n} = a^{m+n}\).
2. Identify the bases and exponents in the given problem. Make sure the bases are the same so you can apply the Product Rule.
3. Add the exponents of the terms with the same base according to the rule: \(m + n\).
4. Rewrite the expression using the base and the new exponent sum: \(a^{m+n}\).
5. If there are multiple terms, repeat the process for each set of like bases, simplifying the expression step by step.