Simplify n^{-5} imes n^{7} imes n^{-1}. Express your answer using positive exponents.
Understand the Problem
The question is asking to simplify the expression involving exponents: n^-5, n^7, and n^-1, and to express the answer using positive exponents.
Answer
The simplified expression is \( n \).
Answer for screen readers
The simplified expression is ( n ).
Steps to Solve
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Combine the Exponents We start with the expression ( n^{-5} \cdot n^{7} \cdot n^{-1} ). According to the exponent multiplication rule, we can combine exponents by adding them: $$ n^{-5 + 7 - 1} $$
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Calculate the Sum of Exponents Now, we simplify the exponent: $$ -5 + 7 - 1 = 1 $$ So, we have: $$ n^{1} $$
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Express with Positive Exponents Since ( n^{1} ) is already in positive exponent form, we can express it simply as: $$ n $$
The simplified expression is ( n ).
More Information
This simplification shows how to add and combine exponents using the properties of exponents. Understanding these rules can greatly aid in performing more complex algebraic manipulations.
Tips
- Neglecting to correctly add or subtract the exponents. Always double-check your arithmetic when combining exponents.
- Forgetting to express the final answer with only positive exponents, as required.
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