Question

How do you find the quotient of `(3r^4)/k^2div(18r^3)/k`?

Answer 1

See the entire solution process below:

Explanation:

First, we can rewrite this expression as:

`((3r^4)/k^2)/((18r^3)/k)`

We can now use this rule for dividing fractions:

`(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))`

`(color(red)(3r^4)/color(blue)(k^2))/(color(green)(18r^3)/color(purple)(k)) = (color(red)(3r^4) xx color(purple)(k))/(color(blue)(k^2) xx color(green)(18r^3)) = (3kr^4)/(18k^2r^3) = (kr^4)/(6k^2r^3)`

We can now use these rules for exponents to further simplify the expression:

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

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

`x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))`

`(kr^4)/(6k^2r^3) = (k^1r^4)/(6k^2r^3) = r^(4-3)/(6k^(2 - 1)) = r^1/(6k^1) = r/(6k)`

Answer 2

`r/(6k)`

Explanation:

To divide by a decimal. multiply by its reciprocal.

`(3r^4)/(k^2) color(blue)(div (18r^3)/k)`

`=(3r^4)/(k^2) color(blue)(xx k/(18r^3))`

`=(cancel3kr^4)/(cancel18_6 k^2r^3)" "larr` subtract indices of like bases

`=r/(6k)`