How do you simplify #(36 m^4 n^3)/(24 m^2 n^5)#?

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Answer 1 · 2015-10-02T09:24:28

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

#(36m^4n^3)/(24m^2n^5)#

#= (cancel36/cancel24) * (m^4n^3)/(m^2n^5)#

#=(3/2) (m^4n^3)/(m^2n^5)#

As per properties:
#color(blue)(1/a=a^-1#

#color(blue)(a^m*a^n=a^(m+n)#

Applying the above properties to #m# and #n#

#=(3/2) m^4n^3 * m^color(blue)(-2)n^color(blue)(-5)#

#=(3/2) * m^color(blue)((4-2)) n^color(blue)((3-5))#

#=(3/2) * m^color(blue)((2)) n^color(blue)((-2))#

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