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To simplify the given expression, we need to follow the rules for manipulating exponents. The expression provided is:

\[
-\frac{1}{x^5} \cdot \frac{1}{x^3} \cdot \frac{1}{x^4}
\]

First, we can use the property of exponents that states \(\frac{1}{a^m} = a^{-m}\):

\[
-\frac{1}{x^5} = -x^{-5}, \quad \frac{1}{x^3} = x^{-3}, \quad \frac{1}{x^4} = x^{-4}
\]

Now we multiply these together:

\[
-x^{-5} \cdot x^{-3} \cdot x^{-4}
\]

Using the property of exponents \(a^m \cdot a^n = a^{m+n}\), we can combine the exponents:

\[
-x^{-5} \cdot x^{-3} \cdot x^{-4} = -x^{-5-3-4} = -x^{-12}
\]

Finally, we convert the negative exponent to a positive exponent:

\[
-x^{-12} = -\frac{1}{x^{12}}
\]

So the simplified expression is:

\[
-\frac{1}{x^{12}}
\]

Would you like more details or have any questions? Here are five related questions for further exploration:

1. How do you multiply two expressions with exponents?
2. What is the rule for combining exponents when multiplying like bases?
3. How do you convert a negative exponent to a positive exponent?
4. Can you apply the same process to simplify the expression \(\frac{2}{x^2} \cdot \frac{3}{x^4} \cdot \frac{5}{x}\)?
5. What is the general rule for simplifying expressions involving multiple terms with exponents?

**Tip:** Always remember that multiplying exponents with the same base involves adding the exponents, and negative exponents indicate reciprocals.

Simplify the expression: -1/(x^5) * 1/(x^3) * 1/(x^4). Write your answer using only positive exponents. Assume that all variables are positive real numbers.

Learn how to simplify the expression -1/(x^5) * 1/(x^3) * 1/(x^4) using positive exponents. This solution covers exponentiation rules and the conversion of negative exponents to positive. Suitable for students in Grades 9-12.

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