How do you simplify #\frac { m ^ { - 2} n ^ { 2} } { 4m ^ { 2} n ^ { 3} }#?

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Answer 1 · 2017-04-13T01:41:21

#(m^-2n^2)/(4m^2n^3)=color(blue)(1/(4m^4n))#

Simplify:

#(m^-2n^2)/(4m^2n^3)#

Apply the negative exponent rule: #b^(-x)=1/(b^x)#.

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

Apply the product rule of exponents: #b^x*b^y=b^(x+y)#

#(n^2)/(4m^((2+2))n^3#

Simplify.

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

Apply quotient rule of exonents: #b^x/b^y=b^(x-y)#.

#(n^(2-3))/(4m^4)#

Simplify.

#n^(-1)/4m^4#

Apply the negative exponent rule: #b^(-x)=1/(b^x)#.

#1/(4m^4n)#