The expression \( \frac{1}{10^{-1}} \) can be simplified as follows:

\[
\frac{1}{10^{-1}} = 10^{1} = 10
\]

This is because dividing by \( 10^{-1} \) is equivalent to multiplying by \( 10^{1} \), which gives you 10.

Would you like further details or have any other questions?

Here are 5 related questions to expand your understanding:

1. What happens if the exponent is positive instead of negative?
2. How do you simplify expressions involving other negative exponents?
3. How can this property be applied to more complex fractions?
4. What are the rules for multiplying and dividing powers of ten?
5. How do negative exponents relate to logarithms?

**Tip:** Negative exponents represent reciprocal values; for example, \( a^{-n} = \frac{1}{a^n} \).

Understand how to simplify the expression one over 10 to the negative 1 (1 / 10^{-1}). This step-by-step solution covers negative exponents, reciprocals, and key exponent rules, ideal for students in Grades 8-10.

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