The given expression is:

$\frac{a^{16}}{b^{-16}}$

To simplify this, we apply the property of exponents that states:

$\frac{x^m}{y^n} = x^m \cdot y^{-n}$

This means that dividing by a negative exponent is equivalent to multiplying by a positive exponent. So:

$\frac{a^{16}}{b^{-16}} = a^{16} \cdot b^{16}$

Thus, the simplified expression is:

$a^{16} \cdot b^{16}$

Or more compactly:

$(a \cdot b)^{16}$

---

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you simplify $\frac{x^a}{x^b}$ using exponent rules?
2. What is the value of $(a^3 \cdot b^2)^4$?
3. How do you handle negative exponents in more complex expressions?
4. What is the general rule for multiplying and dividing powers with the same base?
5. How do you simplify expressions like $\frac{a^{-m}}{b^n}$?

Tip: Remember, a negative exponent flips the base to the denominator or numerator!