The expression given is:

$\sqrt[4]{a^{12}}$

This is asking for the 4th root of $a^{12}$.

To simplify, use the property of radicals and exponents:

$\sqrt[n]{x^m} = x^{m/n}$

Applying this to your expression:

$\sqrt[4]{a^{12}} = a^{12/4} = a^3$

So, the simplified form is:

$a^3$

Would you like further details or have any questions?

Here are some related questions you can explore:

1. What is the general rule for simplifying $\sqrt[n]{x^m}$?
2. How do you simplify $\sqrt[5]{x^{10}}$?
3. What happens when the exponent is not divisible by the root index?
4. How can you rewrite $\sqrt{a^6}$ in terms of exponents?
5. What is the difference between fractional exponents and radicals?

Tip: When simplifying radicals, remember that $\sqrt[n]{x^m} = x^{m/n}$, which helps in converting radical expressions into exponents.