Find the product of :
`3ab^(2),5abc and 2a^(2)c^(3)`

Answer

To find the product of the algebraic expressions \(3ab^2\), \(5abc\), and \(2a^2c^3\), we will follow these steps:

### Step 1: Write down the expressions
We have the following expressions to multiply:
\[ 3ab^2, \quad 5abc, \quad 2a^2c^3 \]

### Step 2: Multiply the numerical coefficients
First, we will multiply the numerical coefficients:
\[ 3 \times 5 \times 2 \]
Calculating this gives:
\[ 3 \times 5 = 15 \]
Then,
\[ 15 \times 2 = 30 \]

### Step 3: Multiply the variables with the same base
Next, we will multiply the variables.

#### For \(a\):
We have:
\[ a^1 \quad (from \, 3ab^2) \quad + \quad a^1 \quad (from \, 5abc) \quad + \quad a^2 \quad (from \, 2a^2c^3) \]
Adding the exponents:
\[ 1 + 1 + 2 = 4 \]
So, we get \(a^4\).

#### For \(b\):
We have:
\[ b^2 \quad (from \, 3ab^2) \quad + \quad b^1 \quad (from \, 5abc) \]
Adding the exponents:
\[ 2 + 1 = 3 \]
So, we get \(b^3\).

#### For \(c\):
We have:
\[ c^1 \quad (from \, 5abc) \quad + \quad c^3 \quad (from \, 2a^2c^3) \]
Adding the exponents:
\[ 1 + 3 = 4 \]
So, we get \(c^4\).

### Step 4: Combine all parts
Now, we can combine all the results:
\[ 30a^4b^3c^4 \]

### Final Answer
Thus, the product of the given expressions is:
\[ \boxed{30a^4b^3c^4} \]

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