Evaluate `(3x^(4)y^(2))(2x^(2)y^(3))` for x = 1 and y = 2.

Answer

To evaluate the expression \((3x^{4}y^{2})(2x^{2}y^{3})\) for \(x = 1\) and \(y = 2\), we will follow these steps:

### Step 1: Substitute the values of \(x\) and \(y\)
We start by substituting \(x = 1\) and \(y = 2\) into the expression.

\[ (3(1)^{4}(2)^{2})(2(1)^{2}(2)^{3}) \]

### Step 2: Simplify the powers
Now, we simplify the powers of \(x\) and \(y\):

\[ (3(1)(2^{2}))(2(1)(2^{3})) \]

Since \(1^{4} = 1\) and \(1^{2} = 1\), we can simplify further:

\[ (3(1)(4))(2(1)(8)) \]

### Step 3: Calculate the values
Now, we calculate the values inside the parentheses:

\[ (3 \cdot 4)(2 \cdot 8) \]

Calculating each part:

\[ 12 \cdot 16 \]

### Step 4: Multiply the results
Finally, we multiply \(12\) and \(16\):

\[ 12 \cdot 16 = 192 \]

### Final Result
Thus, the value of the expression \((3x^{4}y^{2})(2x^{2}y^{3})\) for \(x = 1\) and \(y = 2\) is:

\[ \boxed{192} \]