Expand the Expression: Calculate 6^12 Step by Step

Expand the following equation:

$6^{12}=$

Video Solution

Solution Steps

00:00 Identify the equivalent expressions

00:04 According to the laws of exponents, the multiplication of exponents with the same base (A)

00:07 equals the same base raised to the sum of the exponents (N+M)

00:11 We will apply this formula to our exercise in order to simplify it

00:14 We'll maintain the base and add the exponents together

00:18 We can observe that this expression is not equal to the original expression

00:21 Let's simplify the remaining expressions in the same way

00:31 We can once again observe that this expression is also not equal to the original expression

00:42 This expression is equal to the original expression

00:53 This expression is not equal to the original expression

01:04 This is the solution

Step-by-Step Solution

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 $6^2 \times 6^3 \times 6^7$ .