How do you multiply #(-x^3y^4)(2x^2y^5)#?

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Answer 1 · 2015-12-31T08:41:58

#= -2 x^color(blue)(5) y^color(blue)(9) #

#(-x^3y^4)(2x^2y^5)#

As per the property of exponents :

#color(blue)(a^m xx a^n = a^((m+n))#

Applying the above to the exponents of #x# and #y#

Isolating the negative sign,
#(-x^3y^4)(2x^2y^5) = color(blue)((-1) ) xx (x^3y^4)(2x^2y^5)#

#= color(blue)((-1) ) xx x^color(blue)((3+2)) xx y^color(blue)((4+5)) xx (2) #

#= color(blue)((-1) ) xx 2 xx x^color(blue)((5)) xx y^color(blue)((9)) #

#= -2 xx x^color(blue)((5)) xx y^color(blue)((9)) #

#= -2 x^color(blue)(5) y^color(blue)(9) #