How do you simplify #(45x^4y^8z^7)/(18x^6y^10z^5)#?

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Answer 1 · 2016-09-22T05:41:14

Eliminate common factors in numerator and denominator.

#(45x^4y^8z^7)/(18x^6y^10z^5)# #=# #(cancel9xx5x^4y^8z^7)/(2xxcancel9x^6y^10z^5)# #=# #(5x^4y^8z^7)/(2x^6y^10z^5)# #=# #5/(2x^2)xx1/y^2xxz^2#

#=# #(5z^2)/(2x^2y^2)#

We note that #a^3/a^5# #=# #a^(3-5)# #=# #a^-2# #=# #1/a^2#, alternatively that #a^3/a^5#

#=# #cancel(axxaxxa)/(cancelaxxcancelaxxcancelaxxaxxa)# #=# #1/a^2#

Answer 2 · 2016-09-22T05:45:06

#(45x^4y^8z^7)/(18x^6y^10z^5)=(5z^2)/(2x^2y^2)#

#(45x^4y^8z^7)/(18x^6y^10z^5)#

= #(3xx3xx5xxx^4xxy^8xxz^7)/(2xx3xx3xx x^6xxy^10xxz^5)#

= #(cancel3xxcancel3xx5xxx^4xxy^8xxz^7)/(2xxcancel3xxcancel3xx x^6xxy^10xxz^5)#

= #(5z^(7-5))/(2x^(6-4)y^(10-8))#

= #(5z^2)/(2x^2y^2)#