What is the product of the square of `(1)/(3)` and cube of `(1)/(2)` ?

Answer

To solve the problem of finding the product of the square of \( \frac{1}{3} \) and the cube of \( \frac{1}{2} \), we can follow these steps:

### Step 1: Calculate the square of \( \frac{1}{3} \)
The square of \( \frac{1}{3} \) is calculated as follows:
\[ \left( \frac{1}{3} \right)^2 = \frac{1}{3} \times \frac{1}{3} = \frac{1 \times 1}{3 \times 3} = \frac{1}{9} \]

### Step 2: Calculate the cube of \( \frac{1}{2} \)
The cube of \( \frac{1}{2} \) is calculated as follows:
\[ \left( \frac{1}{2} \right)^3 = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1 \times 1 \times 1}{2 \times 2 \times 2} = \frac{1}{8} \]

### Step 3: Calculate the product of the results from Step 1 and Step 2
Now, we find the product of \( \frac{1}{9} \) and \( \frac{1}{8} \):
\[ \frac{1}{9} \times \frac{1}{8} = \frac{1 \times 1}{9 \times 8} = \frac{1}{72} \]

### Final Answer
Thus, the product of the square of \( \frac{1}{3} \) and the cube of \( \frac{1}{2} \) is:
\[ \frac{1}{72} \]

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