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

Answer

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

### Step 1: Understand the Exponential Form
The expression \(\left(\frac{2}{3}\right)^{4}\) means that we need to multiply \(\frac{2}{3}\) by itself 4 times.

### Step 2: Write the Multiplication
We can express this as:
\[ \left(\frac{2}{3}\right)^{4} = \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \]

### Step 3: Multiply the Numerators
Now, we multiply the numerators (the top parts of the fractions):
\[ 2 \times 2 \times 2 \times 2 = 2^4 = 16 \]

### Step 4: Multiply the Denominators
Next, we multiply the denominators (the bottom parts of the fractions):
\[ 3 \times 3 \times 3 \times 3 = 3^4 = 81 \]

### Step 5: Combine the Results
Now we can combine the results from the numerators and denominators:
\[ \left(\frac{2}{3}\right)^{4} = \frac{16}{81} \]

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