Find the product of cube of `((-3)/(5))` and fourth power of `(2)/(-3)`.

Answer

To find the product of the cube of \((-3/5)\) and the fourth power of \((2/-3)\), we can follow these steps:

### Step 1: Write the expressions with their respective powers
We need to find:
\[ \left(-\frac{3}{5}\right)^3 \times \left(\frac{2}{-3}\right)^4 \]

### Step 2: Calculate the cube of \(-\frac{3}{5}\)
Using the property of exponents:
\[ \left(-\frac{3}{5}\right)^3 = \frac{(-3)^3}{5^3} = \frac{-27}{125} \]

### Step 3: Calculate the fourth power of \(\frac{2}{-3}\)
Similarly, we calculate:
\[ \left(\frac{2}{-3}\right)^4 = \frac{2^4}{(-3)^4} = \frac{16}{81} \]

### Step 4: Multiply the two results
Now we multiply the results from Steps 2 and 3:
\[ \frac{-27}{125} \times \frac{16}{81} = \frac{-27 \times 16}{125 \times 81} \]

### Step 5: Calculate the numerator and denominator
Calculating the numerator:
\[ -27 \times 16 = -432 \]
Calculating the denominator:
\[ 125 \times 81 = 10125 \]

### Step 6: Combine the results
Putting it all together, we get:
\[ \frac{-432}{10125} \]

### Final Answer
Thus, the product of the cube of \((-3/5)\) and the fourth power of \((2/-3)\) is:
\[ \frac{-432}{10125} \]