How do you simplify #(8m^3n^2)/(4mn^3)#?

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Answer 1 · 2018-03-18T14:53:36

See a solution process below:

First, rewrite the expression as:

#8/4(m^3/m)(n^2/n^3) =>#

#2(m^3/m)(n^2/n^3)#

Next, use these rules of exponents to rewrite the #m# terms:

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

#2(m^color(red)(3)/m^color(blue)(1))(n^2/n^3) =>#

#2m^(color(red)(3)-color(blue)(1))(n^2/n^3) =>#

#2m^2(n^2/n^3)#

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

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

#2m^2(n^color(red)(2)/n^color(blue)(3)) =>#

#2m^2(1/n^(color(blue)(3)-color(red)(2))) =>#

#2m^2(1/n^color(red)(1)) =>#

#2m^2(1/n) =>#

#(2m^2)/n#