How do you divide #(12x y ^ { 3} - 9x ^ { 3} y ^ { 7} ) \div ( 3x ^ { 2} y ^ { 5} )#?

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Answer 1 · 2017-09-03T14:21:10

See a solution process below:

First, we can rewrite this expression as:

#a = a^color(red)(1)#

#x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#a^color(red)(1) = a#

#(12xy^3 - 9x^3y^7)/(3x^2y^5) =>#

#(12xy^3)/(3x^2y^5) - (9x^3y^7)/(3x^2y^5) =>#

#(4xy^3)/(x^2y^5) - (3x^3y^7)/(x^2y^5)#

We can now use these rules for exponents to simplify the two terms:

#(4x^color(red)(1)y^color(red)(3))/(x^color(blue)(2)y^color(blue)(5)) - (3x^color(red)(3)y^color(red)(7))/(x^color(blue)(2)y^color(blue)(5)) =>#

#4/(x^(color(blue)(2)-color(red)(1))y^(color(blue)(5)-color(red)(3))) - (3x^(color(red)(3)-color(blue)(2))y^(color(red)(7)-color(blue)(5)))/1 =>#

#4/(x^color(red)(1)y^2) - 3x^color(red)(1)y^2 =>#

#4/(xy^2) - 3xy^2#