How do you multiply #-8x ^ { 6} y ^ { 10} ( - 5x ^ { - 6} y ^ { - 8} )#?

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Answer 1 · 2017-07-16T23:21:28

See a solution process below:

First, rewrite the expression as:

#(-8 * -5)(x^6 * x^-6)(y^10 * y^-8) =>#

#40(x^6 * x^-6)(y^10 * y^-8)#

Next, use this rule to multiply the #x# and #y# terms:

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

#40(x^color(red)(6) * x^color(blue)(-6))(y^color(red)(10) * y^color(blue)(-8)) =>#

#40x^(color(red)(6)+color(blue)(-6))y^(color(red)(10)+color(blue)(-8)) =>#

#40x^(color(red)(6)-color(blue)(6))y^(color(red)(10)-color(blue)(8)) =>#

#40x^0y^2#

Now, use this rule to complete the simplification of the #x# term:

#a^color(red)(0) = 1#

#40x^color(red)(0)y^2 =>#

#(40 * 1)y^2 =>#

#40y^2#