How do you multiply #(6x y ) ( 3x ^ { 9} y ^ { 6} ) #?

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Answer 1 · 2017-10-21T06:11:21

#18x^10y^7#

Multiply the like terms...

#(color(green)(6)color(blue)(x)color(violet)(y))(color(green)(3)color(blue)(x^9)color(violet)(y^6))#

#=>color(green)((6*3))color(blue)((x^1*x^9))color(violet)((y^1*y^6))#

Evaluate using the identity #color(red)(a^b*a^c=a^(b+c)#

#=>(18)(x^(1+9))(y^(1+6))#

#=>18x^10y^7#

Answer 2 · 2017-10-21T06:13:58

#18x^10y^7#

First, you should know that

#a^n*a^m=a^(n+m)#

In this case, we can seperate it to parts at the beginning:

#(6xy)(3x^9y^6)#
#=(6)(x)(y)(3)(x^9)(y^6)#

and we can group the related things together and get the answer
#=(6*3)(x*x^9)(y*y^6)#
#=18*x^(1+9)*y^(1+6)#
#=18x^10y^7#