The value of `((2/5)^(3)xx(1/7)^(3))/((2/5)^(2)xx(1/7)^(4))` is

Options

A. `(2)/35`
B. `(5)/(14)`
C. `14(1)/(2)`
D. `2(4)/(5)`

Answer

To solve the expression \(\frac{(2/5)^{3} \times (1/7)^{3}}{(2/5)^{2} \times (1/7)^{4}}\), we will follow these steps:

### Step-by-Step Solution:

1. **Rewrite the Expression**:
We start with the expression:
\[ \frac{(2/5)^{3} \times (1/7)^{3}}{(2/5)^{2} \times (1/7)^{4}} \]

2. **Apply the Property of Exponents**:
According to the property of exponents, \(\frac{a^m}{a^n} = a^{m-n}\). We can apply this property separately for \((2/5)\) and \((1/7)\):
\[ = \left(\frac{2}{5}\right)^{3-2} \times \left(\frac{1}{7}\right)^{3-4} \]

3. **Simplify the Exponents**:
Now, we simplify the exponents:
\[ = \left(\frac{2}{5}\right)^{1} \times \left(\frac{1}{7}\right)^{-1} \]

4. **Rewrite the Negative Exponent**:
Recall that \(a^{-n} = \frac{1}{a^n}\). Therefore, we can rewrite \(\left(\frac{1}{7}\right)^{-1}\) as:
\[ = \left(\frac{2}{5}\right)^{1} \times 7^{1} \]

5. **Multiply the Terms**:
Now, we can multiply the two fractions:
\[ = \frac{2}{5} \times 7 = \frac{2 \times 7}{5} = \frac{14}{5} \]

6. **Convert to Mixed Fraction**:
To convert \(\frac{14}{5}\) into a mixed fraction:
- Divide 14 by 5, which gives 2 with a remainder of 4.
- Thus, \(\frac{14}{5} = 2 \frac{4}{5}\).

### Final Answer:
The value of the expression is:
\[ 2 \frac{4}{5} \]