Answer:
The given expression \(n^6\cdot n^5\div n^4\cdot n^3\div n^2\cdot n\) is \(n^9\)
Step-by-step explanation:
Given : Expression \(n^6\cdot n^5\div n^4\cdot n^3\div n^2\cdot n\)
We have to write the simplified form for the given expression \(n^6\cdot n^5\div n^4\cdot n^3\div n^2\cdot n\)
Consider the given expression \(n^6\cdot n^5\div n^4\cdot n^3\div n^2\cdot n\)
Rewrite it in simpler form, we have,
\(n^6\cdot\frac{n^5}{n^4}\cdot \frac{n^3}{n^2}\cdot n\)
Apply exponent rule, \(\:a^b\cdot \:a^c=a^{b+c}\), we have,
\(n^6n=\:n^{6+1}\)
\(=\frac{n^5}{n^4}\cdot \frac{n^3}{n^2}n^{7}\)
Apply exponent rule, \(\frac{x^a}{x^b}=x^{a-b}\)
\(\frac{n^5}{n^4}=n^{5-4}\)
\(\frac{n^3}{n^2}=n^{3-2}\)
Expression becomes,
\(=n^7nn\)
Again apply exponent rule, we have,
\(\:a^b\cdot \:a^c=a^{b+c}\)
\(=n^{1+1+7}=n^9\)
Thus, The given expression \(n^6\cdot n^5\div n^4\cdot n^3\div n^2\cdot n\) is \(n^9\)
