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

Question

Abigail Allen · Accepted Answer

See the entire solution process below:

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)#

Eva Abramson · Answer

#r/(6k)#

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)#

Nathan Axel · Answer

undefined To find the quotient of (3r^4)/k^2 divided by (18r^3)/k, we can simplify the expression by dividing the numerator of the first fraction by the numerator of the second fraction, and the denominator of the first fraction by the denominator of the second fraction.

The quotient is given by:

(3r^4/k^2) ÷ (18r^3/k)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

So, the quotient simplifies to:

(3r^4/k^2) × (k/18r^3)

Simplifying further, we can cancel out common factors:

(3r^4 × k) / (k^2 × 18r^3)

This can be simplified to:

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

Further simplifying, we can divide both the numerator and denominator by 3:

r^4k / (6k^2r^3)

Finally, we can simplify by canceling out a common factor of r:

rk / (6k^2r^2)

Therefore, the quotient of (3r^4)/k^2 divided by (18r^3)/k is rk / (6k^2r^2).