How do you simplify #3xy^2z^4 div 9x^2yz^2#?

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Answer 1 · 2016-01-10T15:01:19

#= color(blue)( (x^(-1) y^(1) z^(2))/3#

#(3xy^2z^4)/(9x^2yz^2)#

#= (3/9) (x^1y^2z^4)/(x^2y^1z^2)#

As per property :
#color(blue)(a^m/a^n = a^((m-n))#

Applying the above to exponents of #x ,y# and # z#

#= (3/9) x^((1-2)) y^((2-1)) z^((4-2))#

#= (3/9) x^(-1) y^(1) z^(2)#

#= (cancel3/cancel9) x^(-1) y^(1) z^(2)#

#= color(blue)( (x^(-1) y^(1) z^(2))/3#