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The problem asks which expression is equivalent to \((8^5)^4\).

To solve this, we use the **power of a power** rule, which states:
\[
(a^m)^n = a^{m \cdot n}
\]

In this case, \( a = 8 \), \( m = 5 \), and \( n = 4 \). So:
\[
(8^5)^4 = 8^{5 \cdot 4} = 8^{20}
\]

Thus, the correct expression is \( 8^{20} \).

Would you like more details or have any further questions?

Here are 5 related questions you might find helpful:
1. How do you simplify \((x^3)^5\)?
2. What is the difference between multiplying exponents and raising a power to a power?
3. How would you solve \((3^4)^2\)?
4. Can the power of a power rule be applied to negative exponents?
5. How would you express \((2^2)^n\) in simplified form?

**Tip:** Always remember that when raising a power to another power, you multiply the exponents!

Which expression is equivalent to (8^5)^4?

Discover how to simplify the expression (8^5)^4 using the power of a power rule. This math problem focuses on exponent rules and algebra, ideal for students in Grades 6-8.

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