The value of `6^2 xx 6^(-4) xx 6^8` is

Options

A. `6^6`
B. `6^(-6)`
C. `6^(12)`
D. `6^(-10)`

Answer

To solve the expression \(6^2 \times 6^{-4} \times 6^8\), we can follow these steps:

### Step 1: Identify the Base and Powers
The base in all terms is 6, and the powers are 2, -4, and 8.

### Step 2: Use the Property of Exponents
When multiplying powers with the same base, we can add the exponents. This property is stated as:
\[ a^m \times a^n = a^{m+n} \]
Here, we can apply this property to our expression.

### Step 3: Add the Exponents
Now, we will add the exponents:
\[ 2 + (-4) + 8 \]
Calculating this step-by-step:
- First, add \(2\) and \(-4\):
\[ 2 + (-4) = 2 - 4 = -2 \]
- Next, add \(-2\) and \(8\):
\[ -2 + 8 = 6 \]

### Step 4: Write the Result
Now that we have added the exponents, we can write the expression as:
\[ 6^{2 + (-4) + 8} = 6^6 \]

### Final Answer
Thus, the value of the expression \(6^2 \times 6^{-4} \times 6^8\) is:
\[ \boxed{6^6} \]

---