If `x ne 0 and x=2`, find `x^(4) + (1)/(x^(4))`

Answer

To solve the problem, we need to find the value of \( x^4 + \frac{1}{x^4} \) given that \( x = 2 \).

### Step-by-Step Solution:

1. **Substitute the value of \( x \)**:
\[ x = 2 \]
We need to calculate \( x^4 \) first.

2. **Calculate \( x^4 \)**:
\[ x^4 = 2^4 = 16 \]

3. **Calculate \( \frac{1}{x^4} \)**:
\[ \frac{1}{x^4} = \frac{1}{16} \]

4. **Add \( x^4 \) and \( \frac{1}{x^4} \)**:
\[ x^4 + \frac{1}{x^4} = 16 + \frac{1}{16} \]

5. **Find a common denominator to add the fractions**:
The common denominator between 16 and \( \frac{1}{16} \) is 16. We can rewrite 16 as \( \frac{16 \times 16}{16} \):
\[ 16 = \frac{256}{16} \]

6. **Combine the fractions**:
\[ x^4 + \frac{1}{x^4} = \frac{256}{16} + \frac{1}{16} = \frac{256 + 1}{16} = \frac{257}{16} \]

### Final Answer:
\[ x^4 + \frac{1}{x^4} = \frac{257}{16} \]