What is #(z^2w^-1)^3/((z^3w^2)^2#?

1 Answer
Don't Memorise
Mar 2, 2016

#=color(blue)(w^-7#

Explanation:

  • As per one of the properties of exponents:
    #color(blue)((a^m))^n= a^(mn#

Applying the above to the question in hand:
#((z^2w^-1)^3)/ (z^3w^2)^2#

#= ((z^(2xx3) w^(-1xx3)))/ ((z^(3 xx2 ) w^ ( 2xx 2))#

#= (z^(6) w^(-3))/ (z^(6 ) w^ ( 4)#

#= (cancelz^(6) w^(-3))/ (cancelz^(6 ) w^ ( 4)#

#= ( w^(-3))/ ( w^ ( 4)#

  • As per one of the properties of exponents:
    #color(blue)(a^m/a^n = a^(m-n)#

So, #= ( w^(-3))/ ( w^ ( 4)) = w ^(-3 -4)#

#=color(blue)(w^-7#

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