Find the value of `(3x^(3)) xx (-5xy^(2)) xx (2x^(2)yz^(3))` for x = 1, y = 2 and z = 3.

Answer

To find the value of the expression \( (3x^{3}) \times (-5xy^{2}) \times (2x^{2}yz^{3}) \) for \( x = 1 \), \( y = 2 \), and \( z = 3 \), we will substitute the values of \( x \), \( y \), and \( z \) into the expression and simplify step by step.

### Step 1: Substitute the values into the expression
The expression is:
\[ (3x^{3}) \times (-5xy^{2}) \times (2x^{2}yz^{3}) \]
Substituting \( x = 1 \), \( y = 2 \), and \( z = 3 \):
\[ = (3(1)^{3}) \times (-5(1)(2)^{2}) \times (2(1)^{2}(2)(3)^{3}) \]

### Step 2: Simplify each term
1. Calculate \( 3(1)^{3} \):
\[ 3(1)^{3} = 3 \times 1 = 3 \]

2. Calculate \( -5(1)(2)^{2} \):
\[ -5(1)(2)^{2} = -5 \times 1 \times 4 = -20 \]

3. Calculate \( 2(1)^{2}(2)(3)^{3} \):
\[ 2(1)^{2}(2)(3)^{3} = 2 \times 1 \times 2 \times 27 = 108 \]
(since \( 3^{3} = 27 \))

### Step 3: Combine the results
Now we can combine the results:
\[ = 3 \times (-20) \times 108 \]

### Step 4: Calculate the product
1. First calculate \( 3 \times (-20) \):
\[ 3 \times (-20) = -60 \]

2. Now calculate \( -60 \times 108 \):
\[ -60 \times 108 = -6480 \]

### Final Result
Thus, the value of the expression \( (3x^{3}) \times (-5xy^{2}) \times (2x^{2}yz^{3}) \) for \( x = 1 \), \( y = 2 \), and \( z = 3 \) is:
\[ \boxed{-6480} \]