Simplify the following expressions.
`(x^(3))^(4)`

Answer

To simplify the expression \((x^{3})^{4}\), we will use the exponentiation rule which states that \((a^{m})^{n} = a^{m \cdot n}\).

### Step-by-Step Solution:

1. **Identify the base and the exponents**:
- Here, the base is \(x\), the first exponent is \(3\) (from \(x^{3}\)), and the second exponent is \(4\) (from the outer exponent).

2. **Apply the exponentiation rule**:
- According to the rule, we multiply the exponents:
\[ (x^{3})^{4} = x^{3 \cdot 4} \]

3. **Calculate the multiplication of the exponents**:
- Now, we perform the multiplication:
\[ 3 \cdot 4 = 12 \]

4. **Write the final simplified expression**:
- Therefore, we can write:
\[ (x^{3})^{4} = x^{12} \]

### Final Answer:
\[ x^{12} \]

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