Find the absolute value of
`((2)/(-3))^(4)`

Answer

To find the absolute value of \(\left(\frac{2}{-3}\right)^{4}\), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \left(\frac{2}{-3}\right)^{4} \]
This can be rewritten using the property of exponents:
\[ \frac{2^{4}}{(-3)^{4}} \]

### Step 2: Calculate \(2^{4}\)
Now, we calculate \(2^{4}\):
\[ 2^{4} = 2 \times 2 \times 2 \times 2 = 16 \]

### Step 3: Calculate \((-3)^{4}\)
Next, we calculate \((-3)^{4}\):
\[ (-3)^{4} = (-3) \times (-3) \times (-3) \times (-3) \]
Since multiplying two negative numbers gives a positive number:
\[ (-3) \times (-3) = 9 \quad \text{and} \quad 9 \times 9 = 81 \]
Thus, \((-3)^{4} = 81\).

### Step 4: Combine the results
Now, we can combine the results from Steps 2 and 3:
\[ \frac{2^{4}}{(-3)^{4}} = \frac{16}{81} \]

### Step 5: Find the absolute value
The absolute value of a positive number is the number itself. Since \(\frac{16}{81}\) is already positive, we have:
\[ \text{Absolute value} = \left|\frac{16}{81}\right| = \frac{16}{81} \]

### Final Answer
Therefore, the absolute value of \(\left(\frac{2}{-3}\right)^{4}\) is:
\[ \frac{16}{81} \]

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