How do you simplify #\frac { 2y x ^ { 2} z ^ { - 1} } { x ^ { 4} y ^ { 4} z ^ { 3} }#?

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Answer 1 · 2017-05-25T01:14:41

See a solution process below:

First, rewrite this expression as:

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

Next, use this rule of exponents to simplify the #x# term:

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

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

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

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

Use this same rule to simplify the #z# term:

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

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

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

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

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

Use this same rule and this rule to simplify the #y# term:

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

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

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

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

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

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