How do you simplify #(-3m^4n)/(12m^6n^4)#?

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Answer 1 · 2017-08-02T10:51:01

See a solution process below:

First, rewrite the expression as:

#(-3/12)(m^4/m^6)(n/n^4) => -1/4(m^4/m^6)(n/n^4)#

Next, use this rule of exponents to rewrite the numerator for the #n# term:

#a = a^color(red)(1)#

#-1/4(m^4/m^6)(n^color(red)(1)/n^4)#

Now, use this rule of exponents to complete the simplification for the #m# and #n# terms:

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

#-1/4(m^color(red)(4)/m^color(blue)(6))(n^color(red)(1)/n^color(blue)(4)) =>#

#-1/4(1/m^(color(blue)(6)-color(red)(4)))(1/n^(color(blue)(4)-color(red)(1))) =>#

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

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