How do you multiply #(9a ^ { 4} c ^ { 3} d ^ { 7} ) ( - 2a ^ { - 2} c ^ { - 4} d ^ { 5} )#?

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Answer 1 · 2017-05-23T17:05:53

See a solution process below:

First, rewrite the expression as:

#(9 * -2)(a^4a^-2)(c^3c^-4)(d^7d^5) => -18(a^4a^-2)(c^3c^-4)(d^7d^5)#

Next, use this rule of exponents to multiply each of the variable terms:

#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#-18(a^color(red)(4) xx a^color(blue)(-2))(c^color(red)(3) xx c^color(blue)(-4))(d^color(red)(7) xx d^color(blue)(5)) =>#

#-18(a^(color(red)(4) + color(blue)(-2)))(c^(color(red)(3) + color(blue)(-4)))(d^(color(red)(7) + color(blue)(5))) =>#

#-18a^2c^-1d^12#

Next, use these two rules of exponents to complete the simplification of the #c# variable:

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

#-18a^2c^color(red)(-1)d^12 => (-18a^2d^12)/c^(- color(red)(-1)) => (-18a^2d^12)/c^(color(red)(1) =>#

#(-18a^2d^12)/c#