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