Simplify 6^5 × 6^7: Exponential Multiplication Practice

To solve this problem, we'll follow these steps:

• Step 1: Identify the given expression
• Step 2: Apply the exponent rule for multiplication of powers with the same base
• Step 3: Simplify the expression by adding the exponents

Now, let's work through each step:
Step 1: The given expression is $6^5 \times 6^7$. Here, the base is 6, and the exponents are 5 and 7.
Step 2: We apply the exponent rule, which states that when multiplying two powers with the same base, we add the exponents. Therefore, we have:

$6^5 \times 6^7 = 6^{5+7}$

Step 3: Add the exponents: $5 + 7 = 12$. Thus, the expression simplifies to:

$6^{12}$

Therefore, the solution to the problem is $6^{12}$.