Find the cubes of :
`1(2)/(7)`

Answer

To find the cube of the mixed fraction \(1 \frac{2}{7}\), we will follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
The mixed fraction \(1 \frac{2}{7}\) can be converted to an improper fraction. To do this, we multiply the whole number (1) by the denominator (7) and then add the numerator (2).

\[ 1 \frac{2}{7} = \frac{(1 \times 7) + 2}{7} = \frac{7 + 2}{7} = \frac{9}{7} \]

### Step 2: Find the cube of the improper fraction
Now, we need to find the cube of \(\frac{9}{7}\). The cube of a fraction is found by cubing the numerator and the denominator separately.

\[ \left(\frac{9}{7}\right)^3 = \frac{9^3}{7^3} \]

### Step 3: Calculate \(9^3\) and \(7^3\)
Now we calculate \(9^3\) and \(7^3\):

- \(9^3 = 9 \times 9 \times 9 = 81 \times 9 = 729\)
- \(7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343\)

### Step 4: Write the final answer
Now we can write the cube of the mixed fraction:

\[ \left(1 \frac{2}{7}\right)^3 = \frac{729}{343} \]

### Final Answer:
The cube of \(1 \frac{2}{7}\) is \(\frac{729}{343}\).

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