The expression \((8x^9 c^5)^2\) can be simplified by applying the power rule of exponents, which states that \((a^m)^n = a^{m \cdot n}\).

Let's simplify:

\[
(8x^9 c^5)^2 = 8^2 \cdot (x^9)^2 \cdot (c^5)^2
\]

Now calculate each part:

\[
8^2 = 64
\]

\[
(x^9)^2 = x^{18}
\]

\[
(c^5)^2 = c^{10}
\]

Putting it all together:

\[
64x^{18}c^{10}
\]

So, the simplified form of \((8x^9 c^5)^2\) is:

\[
64x^{18}c^{10}
\]

Would you like more details or have any questions?

### Relative Questions:
1. How does the power rule of exponents work in different cases?
2. What is the result of \((3x^4 y^2)^3\)?
3. Can you explain why \(8^2 = 64\) and not just \(8 \cdot 2\)?
4. How do you simplify expressions with negative exponents?
5. How do fractional exponents work when applied to variables?

**Tip:** When simplifying expressions, always handle each part (coefficients, variables, powers) separately to avoid errors.

Learn how to simplify the expression (8x^9 c^5)^2 using the power rule of exponents. This detailed solution explains the steps involved, covering key algebraic concepts and theorems. Suitable for students in Grades 8-10.

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