How do you simplify #(d/(19f^2))/(d^4/(8f^3))#?

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Answer 1 · 2018-04-06T02:10:14

The simplified expression is #(8f)/(19d^3)#.

When you're dividing fractions by other fractions (called complex fractions), you can use this "trick":

#(color(red)a/color(blue)b)/(color(green)c/color(orange)d)=color(red)a/color(blue)bxxcolor(orange)d/color(green)c#

Here's this trick applied to the expression:

#color(white)=(d/(19f^2))/(d^4/(8f^3))#

#=d/(19f^2)xx(8f^3)/d^4#

#=color(red)cancelcolor(black)d/(19f^2)xx(8f^3)/(d^(color(red)cancelcolor(black)4^3)#

#=1/(19f^2)xx(8f^3)/d^3#

#=1/(19color(red)cancelcolor(black)(f^2))xx(8f^color(red)cancelcolor(black)3)/d^3#

#=1/(19)xx(8f)/d^3#

#=(8f)/(19d^3)#

That's as simplified as it gets. Hope this helped!