Simplify each expression using the product rule if possible.
${12}^3\cdot {12}^9$

• A. ${12}^6$
• B. ${12}^{12}$
• C. ${12}^9$
• D. ${12}^{27}$

Answer: (B)

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 base and the exponents in the given problem. Make sure the bases are the same before applying the rule.
3. Add the exponents together while keeping the base unchanged, according to the rule.
4. Rewrite the expression with the base and the new exponent sum.
5. Simplify the expression if possible, such as reducing the exponent or rewriting the base if needed.