If `a- (1)/(a)= 8 and a ne 0`, find:
`a^(2)- (1)/(a^(2))`

Answer

To solve the problem, we need to find the value of \( a^2 - \frac{1}{a^2} \) given that \( a - \frac{1}{a} = 8 \).

### Step-by-Step Solution:

1. **Start with the given equation:**
\[ a - \frac{1}{a} = 8 \]

2. **Use the identity for \( a^2 - \frac{1}{a^2} \):**
We know that:
\[ a^2 - \frac{1}{a^2} = \left( a - \frac{1}{a} \right)^2 + 2 \]
This can be derived from the expansion of \( (a - \frac{1}{a})^2 \).

3. **Square the left-hand side:**
\[ \left( a - \frac{1}{a} \right)^2 = 8^2 = 64 \]

4. **Substitute into the identity:**
\[ a^2 - \frac{1}{a^2} = 64 + 2 \]

5. **Calculate the final value:**
\[ a^2 - \frac{1}{a^2} = 66 \]

### Final Answer:
\[ a^2 - \frac{1}{a^2} = 66 \]