Simplify : `(3 xx 2)^4`

Answer

To simplify the expression \((3 \times 2)^4\), we can follow these steps:

### Step 1: Identify the expression
We start with the expression:
\[ (3 \times 2)^4 \]

### Step 2: Apply the property of exponents
According to the property of exponents, \((a \times b)^m = a^m \times b^m\). Here, we can let \(a = 3\), \(b = 2\), and \(m = 4\). Therefore, we can rewrite the expression as:
\[ (3 \times 2)^4 = 3^4 \times 2^4 \]

### Step 3: Calculate \(3^4\)
Now, we calculate \(3^4\):
\[ 3^4 = 3 \times 3 \times 3 \times 3 = 9 \times 3 \times 3 = 27 \times 3 = 81 \]

### Step 4: Calculate \(2^4\)
Next, we calculate \(2^4\):
\[ 2^4 = 2 \times 2 \times 2 \times 2 = 4 \times 2 \times 2 = 8 \times 2 = 16 \]

### Step 5: Multiply the results
Now we multiply the results from steps 3 and 4:
\[ 3^4 \times 2^4 = 81 \times 16 \]

### Step 6: Calculate \(81 \times 16\)
To calculate \(81 \times 16\):
\[ 81 \times 16 = 1296 \]

### Final Answer
Thus, the simplified form of \((3 \times 2)^4\) is:
\[ \boxed{1296} \]

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