How do you simplify #\frac { 162x ^ { 2} y ^ { 6} } { - 18x ^ { 6} y ^ { - 9} }#?

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Answer 1 · 2017-10-15T12:27:47

See a solution process below:

First, rewrite the expression as:

#162/-18(x^2/x^6)(y^6/y^-9) =>#

#-9(x^2/x^6)(y^6/y^-9)#

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

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

#-9(x^color(red)(2)/x^color(blue)(6))(y^6/y^-9) =>#

#-9(1/x^(color(blue)(6)-color(red)(2)))(y^6/y^-9) =>#

#-9(1/x^4)(y^6/y^-9) =>#

#-9/x^4(y^6/y^-9)#

Now, use this rule of exponents to simplify the #y# term:

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

#-9/x^4(y^color(red)(6)/y^color(blue)(-9)) =>#

#-9/x^4(y^(color(red)(6)-color(blue)(-9))) =>#

#-9/x^4(y^(color(red)(6)+color(blue)(9))) =>#

#-9/x^4(y^15) =>#

#-(9y^15)/x^4#