Yes, \((5^2)^{-3}\) is the same as \(\frac{1}{5^6}\).

Here’s why:

\[
(5^2)^{-3} = 5^{2 \times (-3)} = 5^{-6}
\]

Now, using the negative exponent rule:

\[
5^{-6} = \frac{1}{5^6}
\]

Thus, \((5^2)^{-3} = \frac{1}{5^6}\).

Would you like further clarification on this? Here are 5 related questions to deepen your understanding:

1. How does the negative exponent rule work in general?
2. What happens when you multiply powers with the same base?
3. How do fractional exponents relate to roots?
4. What are the properties of exponents for non-integer bases?
5. Can you apply exponent rules to complex numbers?

**Tip**: When dealing with exponents, always remember that negative exponents indicate reciprocals.

Explore the relationship between (5^2)^-3 and 1/5^6 using the power of a power and negative exponent rules. This math problem covers key exponent concepts suitable for students in Grades 8-10.

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