How do you simplify #\frac { m ^ { - 2} n ^ { - 4} } { ( 2m ^ { - 2} n ^ { 4} p ^ { - 3} ) ^ { 0} \cdot 2m ^ { 2} n ^ { - 4} p ^ { - 1} }#?

1 Answer
Aviv S.
Mar 12, 2018

The simplified expression is #p/(2m^4)#.

Explanation:

Use these properties:

#x^0=1qquadqquad# (Anything to the power of #0# is #1#)

#x^color(red)m/x^color(blue)n=x^(color(red)m-color(blue)n)#

#1/x^color(red)m=x^(-color(red)m)#

Now here's the problem:

#color(white)=(color(red)(m^-2)color(green)(n^-4))/(color(blue)((2m^-2n^4p^-3)^0)*color(purple)2color(red)(m^2)color(green)(n^-4)color(orange)(p^-1))#

#=(color(red)(m^-2)color(green)(n^-4))/(color(blue)1*color(purple)2color(red)(m^2)color(green)(n^-4)color(orange)(p^-1))#

#=(color(red)(m^-2)color(green)(n^-4))/(color(purple)2color(red)(m^2)color(green)(n^-4)color(orange)(p^-1))#

#=color(purple)1/color(purple)2*color(red)(m^-2)/color(red)(m^2)*color(green)(n^-4)/color(green)(n^-4)*1/color(orange)(p^-1)#

#=color(purple)1/color(purple)2*color(red)(m^-2)/color(red)(m^2)*color(green)(n^-4)/color(green)(n^-4)*color(orange)(p^0)/color(orange)(p^-1)#

#=color(purple)1/color(purple)2*color(red)(m^(-2-2))*color(green)(n^(-4-(-4)))*color(orange)(p^(0-(-1)))#

#=color(purple)1/color(purple)2*color(red)(m^(-4))*color(green)(n^(-4+4))*color(orange)(p^(0+1))#

#=color(purple)1/color(purple)2*color(red)(m^(-4))*color(green)(n^0)*color(orange)(p^1)#

#=color(purple)1/color(purple)2*color(red)(m^(-4))*color(green)1*color(orange)p#

#=color(purple)1/color(purple)2*color(red)(m^(-4))*color(orange)p#

#=color(orange)p/color(purple)2*color(red)(m^(-4))#

#=color(orange)p/color(purple)2*1/color(red)(m^4)#

#=color(orange)p/(color(purple)2color(red)(m^4))#

That's the simplified result. Hope this helped!

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