Question

How do you evaluate `(2n ^ { 7} + 4n ^ { 6} + 4n ^ { 5} ) \div 4n ^ { 2}`?

Answer 1

See the entire solution process below:

Explanation:

First, we can rewrite this expression as:

`(2n^7 + 4n^6 + 4n^5)/(4n^2)`

Which can then be rewritten as:

`(2n^7)/(4n^2) + (4n^6)/(4n^2) + (4n^5)/(4n^2)`

We can then use this rule of exponents to simplify each individual term:

`x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))`

`(2n^color(red)(7))/(4n^color(blue)(2)) + (4n^color(red)(6))/(4n^color(blue)(2)) + (4n^color(red)(5))/(4n^color(blue)(2)) = 1/2n^(color(red)(7)-color(blue)(2)) + 1n^(color(red)(6)-color(blue)(2)) + 1n^(color(red)(5)-color(blue)(2)) =`

`1/2n^5 + n^4 + n^3`

Or

`n^3(1/2n^2 + n + 1)`