Expand the Expression: Calculate 6^12 Step by Step

To solve this problem, let's expand $6^{12}$ as a product of three powers of 6:

• Step 1: Understand that we need three exponents, $a$, $b$, and $c$, such that $a + b + c = 12$.
• Step 2: Check each combination in the choices:
• Choice 1: $6^3 \times 6^2 \times 6^2 \Rightarrow 3 + 2 + 2 = 7$ (not equal to 12)
• Choice 2: $6^4 \times 6^4 \times 6^3 \Rightarrow 4 + 4 + 3 = 11$ (not equal to 12)
• Choice 3: $6^2 \times 6^3 \times 6^7 \Rightarrow 2 + 3 + 7 = 12$ (equal to 12) ✔
• Choice 4: $6^1 \times 6^{11} \times 6 \Rightarrow 1 + 11 + 1 = 13$ (not equal to 12)
• Step 3: Verify that choice 3, $6^2 \times 6^3 \times 6^7$, correctly expands to $6^{12}$ since $6^2 \times 6^3 \times 6^7 = 6^{2+3+7} = 6^{12}$.

Therefore, the correct expansion of $6^{12}$ is $6^2 \times 6^3 \times 6^7$.