How do you divide #\frac { 2x ^ { 4} y ^ { - 4} z ^ { - 3} } { 3x ^ { 2} y ^ { - y } z ^ { 4} }#?

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Answer 1 · 2018-01-25T11:54:09

See a solution process below:

First, rewrite the expression to make it easier to manipulate:

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

Next, use this rule of exponents to divide the #x# and #y# terms:

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

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

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

#2/3x^(color(red)(4)-color(blue)(2))y^(color(red)(-4)+color(blue)(y))(z^-3/z^4) =>#

#2/3x^2y^(-4+y)(z^-3/z^4) =>#

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

Now, use this rule of exponents to divide the #z# term:

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

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

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

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

#2/3x^2y^(y-4)1/z^7 =>#

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