The expression \( 36^{-0.5} \) can be simplified as follows:

1. First, express \( 36^{-0.5} \) as the reciprocal of \( 36^{0.5} \):
   \[
   36^{-0.5} = \frac{1}{36^{0.5}}
   \]
2. \( 36^{0.5} \) is the same as the square root of 36:
   \[
   36^{0.5} = \sqrt{36} = 6
   \]
3. Therefore:
   \[
   36^{-0.5} = \frac{1}{6}
   \]

Thus, \( 36^{-0.5} = \frac{1}{6} \).

Would you like more details, or do you have any questions?

Here are 5 related questions to explore:
1. What is \( 49^{-0.5} \)?
2. How do you simplify \( 25^{0.5} \)?
3. What is the general rule for simplifying \( x^{-n} \)?
4. How does exponentiation affect fractions, e.g., \( \left(\frac{1}{4}\right)^{-0.5} \)?
5. What is \( 100^{-0.5} \)?

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

Learn how to simplify the expression 36^-0.5 step by step using negative exponents and square roots. This example demonstrates how negative exponents represent reciprocals and introduces basic exponent rules, making it ideal for students in Grades 8-10.

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