How do you divide #\frac { 20x ^ { 3} y ^ { 4} } { - 30x ^ { 3} y ^ { 7} }#?

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Answer 1 · 2017-07-21T22:34:05

See a solution process below:

First, rewrite the expression as:

#(-20/30)(x^3/x^3)(y^4/y^7) =>#

#-(2 xx 10)/(3 xx 10)(color(red)(cancel(color(black)(x^3)))/color(red)(cancel(color(black)(x^3))))(y^4/y^7) =>#

#-(2 xx color(red)(cancel(color(black)(10))))/(3 xx color(red)(cancel(color(black)(10)))) * 1 * (y^4/y^7) =>#

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

Now, use this rule for exponents to divide the #y# terms:

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

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

#-2/(3y^3)#