Multiply :
`2 1/3 a^(2) b and 2/7 a^(3)b^(2)`

Answer

To solve the problem of multiplying the expressions \(2 \frac{1}{3} a^2 b\) and \(\frac{2}{7} a^3 b^2\), we can follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
The mixed fraction \(2 \frac{1}{3}\) can be converted to an improper fraction.

\[ 2 \frac{1}{3} = 2 + \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3} \]

### Step 2: Write the multiplication expression
Now we can rewrite the multiplication expression using the improper fraction:

\[ \frac{7}{3} a^2 b \times \frac{2}{7} a^3 b^2 \]

### Step 3: Multiply the coefficients (numerical parts)
Next, we multiply the numerical coefficients:

\[ \frac{7}{3} \times \frac{2}{7} = \frac{7 \times 2}{3 \times 7} = \frac{14}{21} \]

Now, simplify \(\frac{14}{21}\):

\[ \frac{14}{21} = \frac{2}{3} \quad (\text{since } 14 \div 7 = 2 \text{ and } 21 \div 7 = 3) \]

### Step 4: Multiply the variables
Now we multiply the variables \(a^2\) and \(a^3\), and \(b\) and \(b^2\):

\[ a^2 \times a^3 = a^{2+3} = a^5 \]
\[ b \times b^2 = b^{1+2} = b^3 \]

### Step 5: Combine the results
Now, we can combine the results from the coefficients and the variables:

\[ \frac{2}{3} a^5 b^3 \]

### Final Answer
Thus, the final answer is:

\[ \frac{2}{3} a^5 b^3 \]

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