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The problem in the image asks to simplify the following expression and only use positive exponents in the result:

\[
2x^{-4} - 7xy^{-5} \cdot 2x^{-1}y^6
\]

### Steps to simplify:

1. **Distribute the terms in the second part** \( -7xy^{-5} \cdot 2x^{-1}y^6 \):
   \[
   -7xy^{-5} \cdot 2x^{-1}y^6 = -14x^{1-1}y^{-5+6} = -14x^0y^1 = -14y
   \]

2. Now, the expression becomes:
   \[
   2x^{-4} - 14y
   \]

3. **Final step**: Ensure all exponents are positive. The term \( 2x^{-4} \) can be written with a positive exponent:
   \[
   2x^{-4} = \frac{2}{x^4}
   \]

Thus, the fully simplified expression is:

\[
\frac{2}{x^4} - 14y
\]

Would you like more details on any part of the solution?

### Related questions:
1. How do you convert negative exponents into positive exponents?
2. What are the rules for multiplying exponents with the same base?
3. How do you simplify an expression with multiple terms involving exponents?
4. Why does \(x^0 = 1\) for any non-zero \(x\)?
5. How do you handle exponents when distributing over multiplication?

**Tip:** Remember that when multiplying powers with the same base, you add the exponents!

Simplificar: 2x^{-4} - 7xy^{-5} \cdot 2x^{-1}y^6. Utilizar solamente exponentes positivos en la respuesta.

Learn how to simplify the expression 2x^{-4} - 7xy^{-5} \cdot 2x^{-1}y^6 by applying exponent rules and ensuring all exponents are positive. This problem covers essential exponent concepts like the product of powers and negative exponent rules, suitable for students in Grades 9-11.

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