How do you simplify #(c^2/d)/(c^3/d^2)#?

1 Answer
May 19, 2017

Answer:

See a solution process below:

Explanation:

First, use this rule for dividing fractions to rewrite the expression:

#(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)(c^2)/color(blue)(d))/(color(green)(c^3)/color(purple)(d^2)) = (color(red)(c^2) xx color(purple)(d^2))/(color(blue)(d) xx color(green)(c^3)) => (c^2d^2)/(c^3d)#

Now, use these rule of exponents to simplify the #c# terms:

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

#(c^color(red)(2)d^2)/(c^color(blue)(3)d) => d^2/(c^(color(blue)(3)-color(red)(2))d) => d^2/(c^1d) => d^2/(cd)#

Now, use these rules of exponents to simplify the #d# terms:

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

#d^2/(cd) => d^color(red)(2)/(cd^color(blue)(1)) => d^(color(red)(2)-color(blue)1)/c => d^1/c => d/c#