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​(Simplify your answer. Type an integer or a​ fraction.)

The expression given is:

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

To simplify, we can use the property of exponents that states:

\[
a^{-n} = \frac{1}{a^n}
\]

In this case, we have \( 6^{-5} \), so we rewrite it as:

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

Now, calculate \( 6^5 \):

\[
6^5 = 7776
\]

Therefore, the simplified expression is:

\[
7776
\]

Would you like more details or have any questions? Here are some related questions to consider:

1. How do you simplify other negative exponents like \( x^{-3} \)?
2. What is the general rule for handling negative exponents in fractions?
3. How does \( a^{-n} \) relate to reciprocal properties?
4. What are the steps to calculate powers of a number, like \( 6^5 \)?
5. How do you simplify expressions that involve both positive and negative exponents?

**Tip:** When simplifying expressions with negative exponents, remember to rewrite the negative exponent as a positive one by taking the reciprocal of the base.

Learn how to simplify the expression 1/6^(-5) using the negative exponent rule. This math problem covers key exponentiation concepts and simplifies the expression to 7776. Suitable for students in Grades 8-10.

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