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

2 Answers
Oct 21, 2017

18x^10y^7

Explanation:

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

Oct 21, 2017

18x^10y^7

Explanation:

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