How do you simplify #\frac { 36w x ^ { 3} } { 9w ^ { 2} x ^ { 4} }#?

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Answer 1 · 2017-08-05T11:38:15

See a solution process below:

First, rewrite the expression as:

#(36/9)(w/w^2)(x^3/x^4) => 4(w/w^2)(x^3/x^4)#

Use this rule of exponents to rewrite the #w# variable in the numerator:

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

#4(w^color(red)(1)/w^2)(x^3/x^4)#

Now, use these rules of exponents to simplify the #w# and #x# terms:

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

#4(w^color(red)(1)/w^color(blue)(2))(x^color(red)(3)/x^color(blue)(4)) =>#

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

#4(1/w^1)(1/x^1) =>#

#4(1/w)(1/x) =>#

#4/(wx)#