Find the product of :
`-4xy^(2) , 5/2xz^(3) and - 3yz `

Answer

To find the product of the expressions \(-4xy^2\), \(\frac{5}{2}xz^3\), and \(-3yz\), we will follow these steps:

### Step 1: Multiply the numerical coefficients
We start by multiplying the numerical coefficients from each expression:
\[ -4 \times \frac{5}{2} \times -3 \]

### Step 2: Calculate the product of the coefficients
First, we simplify the multiplication:
1. Multiply \(-4\) and \(-3\):
\[ -4 \times -3 = 12 \]
2. Now multiply \(12\) by \(\frac{5}{2}\):
\[ 12 \times \frac{5}{2} = \frac{12 \times 5}{2} = \frac{60}{2} = 30 \]

### Step 3: Multiply the variables
Next, we multiply the variable parts:
1. For \(x\):
\[ x \text{ (from } -4xy^2\text{)} \times x \text{ (from } \frac{5}{2}xz^3\text{)} = x^2 \]
2. For \(y\):
\[ y^2 \text{ (from } -4xy^2\text{)} \times y \text{ (from } -3yz\text{)} = y^{2+1} = y^3 \]
3. For \(z\):
\[ z^3 \text{ (from } \frac{5}{2}xz^3\text{)} \times z \text{ (from } -3yz\text{)} = z^{3+1} = z^4 \]

### Step 4: Combine the results
Now we combine the results from steps 2 and 3:
\[ 30x^2y^3z^4 \]

### Final Answer
Thus, the product of the expressions is:
\[ 30x^2y^3z^4 \]