Evaluate `(1""2/5)^(3)`

Answer

To evaluate \( (1 \frac{2}{5})^3 \), we will follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
A mixed fraction \( 1 \frac{2}{5} \) can be converted to an improper fraction using the formula:
\[ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator} + \text{Numerator}\right) / \text{Denominator} \]
For \( 1 \frac{2}{5} \):
\[ 1 \frac{2}{5} = \frac{1 \times 5 + 2}{5} = \frac{5 + 2}{5} = \frac{7}{5} \]

### Step 2: Cube the improper fraction
Now we need to cube the improper fraction \( \frac{7}{5} \):
\[ \left(\frac{7}{5}\right)^3 = \frac{7^3}{5^3} \]

### Step 3: Calculate \( 7^3 \) and \( 5^3 \)
Calculating \( 7^3 \):
\[ 7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343 \]
Calculating \( 5^3 \):
\[ 5^3 = 5 \times 5 \times 5 = 25 \times 5 = 125 \]

### Step 4: Combine the results
Now we can combine the results from the cubing:
\[ \left(\frac{7}{5}\right)^3 = \frac{343}{125} \]

### Final Answer
Thus, the evaluation of \( (1 \frac{2}{5})^3 \) is:
\[ \frac{343}{125} \]

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