Simplify \( \frac{w^{-1}}{w} \) and express your answer using positive exponents.

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Understand the Problem

The question asks to simplify the expression ( \frac{w^{-1}}{w} ) and express the answer using positive exponents. This requires understanding of exponent rules, particularly dealing with negative exponents.

Answer

The simplified expression is \( \frac{1}{w^2} \).
Answer for screen readers

The simplified expression is ( \frac{1}{w^2} ).

Steps to Solve

  1. Identify the expression to simplify We start with the expression ( \frac{w^{-1}}{w} ).

  2. Apply the laws of exponents Using the rule ( \frac{a^m}{a^n} = a^{m-n} ), we can rewrite the expression as follows: $$ \frac{w^{-1}}{w} = w^{-1 - 1} = w^{-2} $$

  3. Convert to positive exponent To express ( w^{-2} ) using positive exponents, we use the rule ( a^{-n} = \frac{1}{a^n} ): $$ w^{-2} = \frac{1}{w^2} $$

The simplified expression is ( \frac{1}{w^2} ).

More Information

Simplifying expressions with negative exponents is a common practice in algebra. It helps in making expressions easier to read and work with. This particular example highlights the conversion from a negative to a positive exponent.

Tips

  • Confusing the subtraction in the exponent rule, which may lead to incorrect simplification such as ( w^{-2} ) being written as ( w^2 ) instead.
  • Forgetting to convert negative exponents into their positive form.

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