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

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Answer 1 · 2016-11-02T20:40:27

#2mn^17p^12#

Recall: #(x^m)^n = x^(mn)#

#x^-m = 1/x^m and 1/x^-m = x^m#

#x^m xx x^n = x^(m+n)#

#x^m/x^n = x^(m-n)#

#(2mn^2p^4 )/((mn^4p^3)^color(red)(-4)xx(nm^4p^4))" "larr# attend to negative index

# = ((2mn^2p^4 )xxcolor(blue)((mn^4p^3))^color(red)(4))/(nm^4p^4)" "larr# remove the bracket

#= ((2mn^2p^4 )xxcolor(blue)((m^4n^16p^12)))/(nm^4p^4)" "larr# simplify numerator

#=(2m^5n^18p^16)/(nm^4p^4)" "larr# subtract indices of like bases

=#2mn^17p^12#