Simplify \( \frac{w^0}{w} \). Express your answer using positive exponents.
Understand the Problem
The question is asking to simplify the expression ( \frac{w^0}{w} ) and to express the answer using positive exponents.
Answer
The simplified expression is \( \frac{1}{w} \).
Answer for screen readers
The simplified expression is ( \frac{1}{w} ).
Steps to Solve
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Simplify the expression with (w^0) Recall that any non-zero number raised to the power of 0 equals 1. Therefore, we have: $$ w^0 = 1 $$
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Rewrite the expression Replace (w^0) in the original expression: $$ \frac{w^0}{w} = \frac{1}{w} $$
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Express using positive exponents The expression (\frac{1}{w}) can also be written using a negative exponent: $$ \frac{1}{w} = w^{-1} $$ However, since the question asks for positive exponents, the final expression is: $$ w^{-1} = \frac{1}{w} $$
The simplified expression is ( \frac{1}{w} ).
More Information
This simplification process highlights the rule that (w^0 = 1) and emphasizes that using negative exponents can also lead to different forms of the same expression. In contexts where only positive exponents are needed, expressing the result as ( \frac{1}{w} ) is appropriate.
Tips
- Confusing (w^0) with (0): Remember that (w^0) equals 1, not 0.
- Neglecting the need for positive exponents: Ensure the final answer is expressed in a form with positive exponents where required.
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