To simplify $(3^5)^4$ to a single power of $3$, use the power of a power property, which states:

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

Here, $a = 3$, $m = 5$, and $n = 4$. Applying the property:

$(3^5)^4 = 3^{5 \cdot 4} = 3^{20}.$

Final Answer:

$(3^5)^4 = 3^{20}.$

Would you like to see more examples of simplifying powers or ask further questions?

Related Questions:

1. What is the expanded form of $3^{20}$?
2. How is the power of a power property derived?
3. Can you explain other exponent rules like the product of powers or the quotient of powers?
4. How do you simplify expressions with multiple bases, like $(2^3 \cdot 3^2)^4$?
5. What is the difference between $(a^m)^n$ and $a^{m+n}$?

Tip:

When working with exponents, always check the base and operations first—this helps ensure you apply the correct rules efficiently!