To solve \((5^4)^3\), you apply the power of a power rule, which states that \((a^m)^n = a^{m \cdot n}\). Here, the base is \(5\), and the exponents are \(4\) and \(3\).

\[
(5^4)^3 = 5^{4 \cdot 3} = 5^{12}
\]

Now, calculating \(5^{12}\):

\[
5^{12} = 244140625
\]

So, \((5^4)^3 = 244140625\).

Would you like further details or any clarifications? Here are 5 questions to deepen understanding:

1. How does the power of a power rule work for negative exponents?
2. Can you explain how to solve \((3^2)^4\) using the same method?
3. What would change in the calculation if the base were a fraction?
4. How do you calculate powers of numbers without a calculator?
5. What is the general rule for simplifying \((x^a)^b\)?

**Tip:** The power of a power rule is a shortcut to simplify expressions quickly, avoiding unnecessary intermediate calculations!

Learn how to simplify the exponent expression (5^4)^3 using the Power of a Power Rule. This step-by-step guide covers exponent rules and explains how to calculate 5^12. Suitable for students in Grades 6-8.

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