How do you divide #\frac { 60x ^ { - 9} y ^ { - 5} } { - 4x ^ { - 6} y ^ { - 4} }#?

1 Answer
smendyka
Jul 18, 2017

See a solution process below:

Explanation:

First, rewrite the expression as:

#(60/-4)(x^-9/x^-6)(y^-5/y^-4) =>#

#-15(x^-9/x^-6)(y^-5/y^-4)#

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

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

#-15(x^color(red)(-9)/x^color(blue)(-6))(y^color(red)(-5)/y^color(blue)(-4)) => -15(1/x^(color(blue)(-6)-color(red)(-9)))(1/y^(color(blue)(-4)-color(red)(-5))) =>#

#-15(1/x^(color(blue)(-6)+color(red)(9)))(1/y^(color(blue)(-4)+color(red)(5))) =>#

#-15(1/x^3)(1/y^1) =>#

#-15/(x^3y^1)#

We can now use this rule of exponents to simplify the #y# term:

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

#-15/(x^3y^color(red)(1)) =>#

#-15/(x^3y)#

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