How do you simplify #\frac { - 3m ^ { 5} n ^ { 4} } { 2m ^ { - 6} n ^ { 0} }#?

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Answer 1 · 2018-01-20T23:56:44

See a solution process below:

First, rewrite the expression as:

#(-3/2)(m^5/m^-6)(n^4/n^0) => -3/2(m^5/m^-6)(n^4/n^0)#

Next, use this rule of exponents to simplify the #m# term:

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

#-3/2(m^color(red)(5)/m^color(blue)(-6))(n^4/n^0) =>#

#-3/2(m^(color(red)(5)-color(blue)(-6)))(n^4/n^0) =>#

#-3/2(m^(color(red)(5)+color(blue)(6)))(n^4/n^0) =>#

#-3/2(m^11)(n^4/n^0) =>#

#(-3m^11)/2(n^4/n^0)#

Now, use this rule of exponents to simplify the #n# term:

#a^color(red)(0) = 1#

#(-3m^11)/2(n^4/n^color(red)(0)) =>#

#(-3m^11)/2(n^4/1) =>#

#(-3m^11)/2(n^4) =>#

#(-3m^11n^4)/2#