Simplify the Product: 6³ × 6⁵ × 6⁶ × 6⁴ Using Laws of Exponents

Reduce the following equation:

$6^3\times6^5\times6^6\times6^4=$

To solve this problem, we will apply the rule for multiplying powers with the same base. This rule states that when multiplying like bases, we can add the exponents. Let's break down the steps:

• Step 1: Identify the exponents of each power of $6$. They are $3$, $5$, $6$, and $4$.
• Step 2: Add these exponents together. This gives us $3 + 5 + 6 + 4$.
• Step 3: Calculate the sum: $3 + 5 + 6 + 4 = 18$.
• Step 4: Write the result as a single power: $6^{18}$.

Thus, by applying the rule for the multiplication of powers, the entire expression simplifies to $6^{18}$.

The correct answer is therefore $6^{18}$, which corresponds with the choice labeled "1" in the given options.