What is the number of terms in the expansion of the following?
`[ ( x-2)^(3) ]^3`

Answer

To find the number of terms in the expansion of \((x - 2)^3\) raised to the power of 3, we can follow these steps:

### Step 1: Simplify the expression
We start with the expression \([(x - 2)^3]^3\). According to the laws of exponents, we can multiply the exponents:

\[ [(x - 2)^3]^3 = (x - 2)^{3 \cdot 3} = (x - 2)^9 \]

### Step 2: Identify the form of the binomial expansion
The expression \((x - 2)^9\) is a binomial expression of the form \((a + b)^n\), where \(a = x\), \(b = -2\), and \(n = 9\).

### Step 3: Use the formula for the number of terms in a binomial expansion
The number of terms in the expansion of \((a + b)^n\) is given by the formula:

\[ \text{Number of terms} = n + 1 \]

### Step 4: Apply the formula
In our case, \(n = 9\). Therefore, the number of terms in the expansion of \((x - 2)^9\) is:

\[ 9 + 1 = 10 \]

### Final Answer
Thus, the number of terms in the expansion of \([(x - 2)^3]^3\) is **10**.

---