How do you simplify #(((-m^4)(p^4)(q^4))^-1 ) /((m)(q)(p^3) x (m^3)(p^-3)(q^-1)#?

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Answer 1 · 2017-06-25T17:57:30

#color(blue)(1/(-m^8p^4q^4x)#

#((-m^4)(p^4)(q^4))^-1/((m)(q)(p^3)x(m^3)(p^-3)(q^-1))#

#:.=(1/(-m^4*p^4*q^4))/(m*q*p^3*x*m^3*p^-3*q^-1)#

#:.=(1/(-m^4*p^4*q^4))/(m^(1+3)*q^(1-1)*p^(3-3)*x)#

#:.=(1/(-m^4*p^4*q^4))/(m^4*q^0*p^0*x)#

#:.=(1/(-m^4*p^4*q^4))/(m^4*1*1*x)#

#:.=(1/(-m^4*p^4*q^4))/(m^4*x)#

#:.=1/(-m^4*p^4*q^4) xx 1/(m^4*x)#

#:.=1/(-m^(4+4)*p^4*q^4*x) #

#:.color(blue)(=1/(-m^8*p^4*q^4*x) #

Answer 2 · 2017-06-25T19:23:22

#-1/(m^8p^4q^4)#

I suspect the #x# was meant to be #xx#?

Simplify where possible first in the numerator and denominator separately.

#((-m^4)(p^4)(q^4))^-1/((m)(q)(p^3)xx(m^3)(p^-3)(q^-1))#

#=((-m^-4)(p^-4)(q^-4))/((m^4)(q^0)(p^0))" "(larr"multiply the indices by -1")/(larr "add the indices of like bases")#

#x^0 = 1 and x^-m = 1/x^m#

#-1/(m^4 m^4p^4q^4)#

#-1/(m^8p^4q^4)#