Let's simplify the expression:

\[
\left(\frac{p^5}{6^5}\right)^{-2}
\]

### Step 1: Apply the power rule

When you have a power raised to another power, multiply the exponents:

\[
\left(\frac{p^5}{6^5}\right)^{-2} = \frac{(p^5)^{-2}}{(6^5)^{-2}} = \frac{p^{-10}}{6^{-10}}
\]

### Step 2: Simplify the negative exponents

To simplify, recall that \(a^{-n} = \frac{1}{a^n}\):

\[
\frac{p^{-10}}{6^{-10}} = \frac{1}{p^{10}} \times 6^{10} = \frac{6^{10}}{p^{10}}
\]

Thus, the completely simplified expression is:

\[
\frac{6^{10}}{p^{10}}
\]

Would you like further details or any clarifications?

Here are 5 related questions:
1. How do you simplify expressions with multiple negative exponents?
2. What happens if you raise a fraction to a negative power?
3. How can you simplify \(\left(\frac{x^2}{y^3}\right)^{-4}\)?
4. What is the general rule for raising powers to powers?
5. How do you handle variables in the denominator with negative exponents?

**Tip**: Negative exponents represent the reciprocal of the base raised to the positive exponent.

Learn how to simplify the expression ((p^5)/(6^5))^-2 using the laws of exponents. This step-by-step guide demonstrates the power of a power rule and how to handle negative exponents. Perfect for students in Grades 9-12.

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