Question
Simplify \( n^{6}-n^{5} \div n^{4} \cdot n^{3} \div n^{2}-n \) \( n \)
Ask by Sanders Li. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( n^{6}-n^{2}-n \).
Solution
Calculate or simplify the expression \( n^6-n^5/n^4*n^3/n^2-n \).
Simplify the expression by following steps:
- step0: Solution:
\(n^{6}-\frac{\frac{n^{5}}{n^{4}}\times n^{3}}{n^{2}}-n\)
- step1: Divide the terms:
\(n^{6}-\frac{n\times n^{3}}{n^{2}}-n\)
- step2: Reduce the fraction:
\(n^{6}-n^{2}-n\)
The simplified expression is \( n^{6}-n^{2}-n \).
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Simplify this solution Beyond the Answer
To simplify the expression \( n^{6}-n^{5} \div n^{4} \cdot n^{3} \div n^{2}-n \), we start with the division operations: 1. Calculate \( n^5 \div n^4 = n^{5-4} = n^1 = n \). 2. Next, calculate \( n \cdot n^3 \div n^2 \): - First, \( n \cdot n^3 = n^{1+3} = n^4 \). - Then, \( n^4 \div n^2 = n^{4-2} = n^2 \). Now substituting back, the expression becomes: \( n^{6} - n^{2} - n \). Next, combine like terms: 1. Rewrite \( n^6 \) and \( -n^2 - n \): The final simplified expression is: \( n^{6} - n^{2} - n \).
