How do you simplify #\frac { 16x y ^ { 3} } { 8x ^ { 2} y }#?

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Answer 1 · 2017-05-30T14:25:11

See a solution process below:

First, rewrite this expression as:

#(16/8)(x/x^2)(y^3/y) => 2(x/x^2)(y^3/y)#

Next, we can use these rules of exponents to simplify the #x# term:

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

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

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

We can now use these rules of exponents to simplify the #y# term:

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

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