To factor the expression $16x^{4a} - y^{8a}$, we recognize that it is a difference of squares, which can be factored using the identity:

$A^2 - B^2 = (A - B)(A + B)$

Here, we can rewrite the expression as:

$(4x^{2a})^2 - (y^{4a})^2$

Using the difference of squares identity, we get:

$16x^{4a} - y^{8a} = (4x^{2a} - y^{4a})(4x^{2a} + y^{4a})$

So, the fully factored form of the expression is:

$\boxed{(4x^{2a} - y^{4a})(4x^{2a} + y^{4a})}$

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you factor the expression $x^4 - y^4$?
2. What is the difference of squares formula, and how is it applied?
3. How would you factor $9x^{6} - 25y^{2}$?
4. Can you explain how to factor $a^2 - 2ab + b^2$?
5. What is the process to factor $x^8 - 1$?

Tip: When factoring expressions, always check if the terms can be rewritten as perfect squares, as it often leads to a difference of squares.