The given expression is $(x^8)^{-4}$ and it is rewritten as $x^a$. We need to find the value of $a$.

To solve this, we apply the rule of exponents that states:

$(a^m)^n = a^{m \cdot n}$

In this case:

$(x^8)^{-4} = x^{8 \cdot (-4)} = x^{-32}$

Thus, the expression becomes $x^{-32}$, which means $a = -32$.

The value of $a$ is $-32$.

Do you need any further details or have any questions?

Here are 5 related questions for practice:

1. Simplify $(x^5)^{-3}$.
2. What is the value of $a$ if $(x^{12})^b = x^{36}$?
3. Rewrite $(x^3)^5$ using a single exponent.
4. If $(y^4)^{-2} = y^a$, what is the value of $a$?
5. What is the result of $(z^7)^{0}$?

Tip: When simplifying expressions with exponents, always remember the power of a power rule: $(a^m)^n = a^{m \cdot n}$.