The expression \( \frac{x^{-5}}{y^6} \) can be simplified using the rules of exponents.

### Step-by-step explanation:

1. **Negative exponent rule**: 
   The negative exponent indicates the reciprocal. So, \( x^{-5} \) can be written as \( \frac{1}{x^5} \).

2. **Rewrite the expression**: 
   Using this rule, we rewrite the expression:
   \[
   \frac{x^{-5}}{y^6} = \frac{1}{x^5 y^6}
   \]

So, the simplified expression is:
\[
\frac{1}{x^5 y^6}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you simplify expressions with multiple negative exponents?
2. What is the power of a product rule for exponents?
3. How do you simplify \( \frac{x^m}{x^n} \) when \( m \) and \( n \) are different?
4. What happens when the exponent is zero in an expression like \( x^0 \)?
5. How can exponents be applied in real-world problems like population growth?

**Tip**: Remember, when multiplying terms with the same base, you can add their exponents!

This tutorial explains how to simplify the expression x^-5/y^6 using the rules of exponents. Learn step-by-step how to handle negative exponents and rewrite the expression as 1/(x^5 * y^6). This problem is suitable for students in Grades 8-10.

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