Use properties of determinants to evaluate :
`|{:(2,3,5),(261,127,388),(20,30,50):}|`

Answer

To evaluate the determinant \( | \begin{vmatrix} 2 & 3 & 5 \\ 261 & 127 & 388 \\ 20 & 30 & 50 \end{vmatrix} | \) using properties of determinants, we can follow these steps:

### Step 1: Write the determinant
We start with the given determinant:

\[ D = \begin{vmatrix} 2 & 3 & 5 \\ 261 & 127 & 388 \\ 20 & 30 & 50 \end{vmatrix} \]

### Step 2: Apply the property of determinants
We notice that if we add the first column (C1) to the second column (C2), we can see if it results in the third column (C3). Let's perform this operation:

- New C2 = C1 + C2
- New C2 values:
- First row: \( 2 + 3 = 5 \)
- Second row: \( 261 + 127 = 388 \)
- Third row: \( 20 + 30 = 50 \)

So, we can rewrite the determinant as:

\[ D = \begin{vmatrix} 2 & 5 & 5 \\ 261 & 388 & 388 \\ 20 & 50 & 50 \end{vmatrix} \]

### Step 3: Identify identical columns
Now, we observe that the second and third columns (C2 and C3) are identical:

\[ \begin{vmatrix} 2 & 5 & 5 \\ 261 & 388 & 388 \\ 20 & 50 & 50 \end{vmatrix} \]

### Step 4: Apply the property of identical columns
According to the properties of determinants, if two columns (or rows) of a determinant are identical, the value of the determinant is zero. Therefore:

\[ D = 0 \]

### Final Answer
Thus, the value of the determinant is:

\[ \boxed{0} \]