`(2/3)^(3)xx(5/7)^(3)` is equal to

Options

A. `(2/3xx5/7)^(9)`
B. `(2/3xx5/7)^(6)`
C. `(2/3xx5/7)^(3)`
D. `(2/3xx5/7)^(@)`

Answer

To solve the expression \((\frac{2}{3})^{3} \times (\frac{5}{7})^{3}\), we can use the property of exponents that states if the bases are different but the exponents are the same, we can combine them. Here’s how to do it step by step:

### Step-by-Step Solution:

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

2. **Use the Exponent Property**:
Since both terms are raised to the power of 3, we can use the property of exponents:
\[ a^{m} \times b^{m} = (a \times b)^{m} \]
Here, \(a = \frac{2}{3}\) and \(b = \frac{5}{7}\).

3. **Combine the Bases**:
We can combine the bases:
\[ \left(\frac{2}{3} \times \frac{5}{7}\right)^{3} \]

4. **Multiply the Fractions**:
Now, we multiply the fractions:
\[ \frac{2 \times 5}{3 \times 7} = \frac{10}{21} \]

5. **Raise to the Power**:
Now we raise the result to the power of 3:
\[ \left(\frac{10}{21}\right)^{3} \]

6. **Final Expression**:
The final expression is:
\[ \frac{10^{3}}{21^{3}} = \frac{1000}{9261} \]

### Final Answer:
Thus, the expression \((\frac{2}{3})^{3} \times (\frac{5}{7})^{3}\) is equal to:
\[ \left(\frac{10}{21}\right)^{3} \]