To simplify $(x^4)^3$, use the power of a power rule:

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

Applying this rule:

$(x^4)^3 = x^{4 \cdot 3} = x^{12}$

Final Answer:

$x^{12}$

Would you like a more detailed explanation?

Related Questions:

1. How do you simplify $(x^2)^5$?
2. What is the difference between the power of a power rule and the power of a product rule?
3. How do you expand $(xy^2)^4$?
4. What happens when the exponent is negative, like $(x^3)^{-2}$?
5. Can you explain how to simplify $(2x^3)^4$?

Tip:

When raising an exponent to another exponent, always multiply the exponents.