Question

How do you simplify `(n^2 times n^3) /n^4`?

Answer 1

`n`

Explanation:

First, we can simplify the numerator using the rule for exponents which states:

`(x^color(red)(a)) xx (x^color(blue)(b)) = x^(color(red)(a) + color(blue)(b))`

`(n^color(red)(2) xx n^color(blue)(3))/n^4 = n^(color(red)(2) + color(blue)(3))/n^4 = n^5/n^4`

Now, we can use another rule for exponents to simplify even further:

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

`(n^color(red)(5))/(n^color(blue)(4)) = x^(color(red)(5) - color(blue)(4)) = n^1`

Finally, we can use one last rule for exponents to complete the simplification of this expression:

`color(red)(x^1 = x)`

`n^1 = n`