Answer in one word
` |{:(3,1,9),(5,2,15),(7,4,21):}|`.

Answer

To solve the given determinant \( | \begin{vmatrix} 3 & 1 & 9 \\ 5 & 2 & 15 \\ 7 & 4 & 21 \end{vmatrix} | \), we will follow these steps:

### Step 1: Identify the determinant
The determinant is given as:
\[ D = \begin{vmatrix} 3 & 1 & 9 \\ 5 & 2 & 15 \\ 7 & 4 & 21 \end{vmatrix} \]

### Step 2: Factor out common elements
Notice that the third column can be expressed as multiples of 3:
- \( 9 = 3 \times 3 \)
- \( 15 = 3 \times 5 \)
- \( 21 = 3 \times 7 \)

Thus, we can factor out 3 from the third column:
\[ D = 3 \cdot \begin{vmatrix} 3 & 1 & 3 \\ 5 & 2 & 5 \\ 7 & 4 & 7 \end{vmatrix} \]

### Step 3: Observe identical columns
Now, observe that the third column \( \begin{pmatrix} 3 \\ 5 \\ 7 \end{pmatrix} \) is identical to the first column \( \begin{pmatrix} 3 \\ 5 \\ 7 \end{pmatrix} \) after factoring out 3.

### Step 4: Apply the property of determinants
If any two columns (or rows) of a determinant are identical, the value of the determinant is zero:
\[ D = 3 \cdot 0 = 0 \]

### Step 5: Final answer
Thus, the value of the determinant is:
\[ \boxed{0} \]

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