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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.

Simplify the expression 4th root of a^12.

Learn how to simplify the expression sqrt[4]{a^12} by applying the laws of exponents and radicals. This problem is suitable for high school students in Grades 9-10 and covers key algebraic concepts such as exponents and radical expressions.

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