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

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

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Answer 1 · 2017-10-21T06:11:21

$18 x^{10} y^{7}$ $18x^10y^7$

Explanation:

Multiply the like terms...

$(6 x y) (3 x^{9} y^{6})$ $(color(green)(6)color(blue)(x)color(violet)(y))(color(green)(3)color(blue)(x^9)color(violet)(y^6))$

$\Rightarrow (6 \cdot 3) (x^{1} \cdot x^{9}) (y^{1} \cdot y^{6})$ $=>color(green)((6*3))color(blue)((x^1*x^9))color(violet)((y^1*y^6))$

Evaluate using the identity $a^{b} \cdot a^{c} = a^{b + c}$ $color(red)(a^b*a^c=a^(b+c)$

$\Rightarrow (18) (x^{1 + 9}) (y^{1 + 6})$ $=>(18)(x^(1+9))(y^(1+6))$

$\Rightarrow 18 x^{10} y^{7}$ $=>18x^10y^7$

Answer 2 · 2017-10-21T06:13:58

$18 x^{10} y^{7}$ $18x^10y^7$

Explanation:

First, you should know that

$a^{n} \cdot a^{m} = a^{n + m}$ $a^n*a^m=a^(n+m)$

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

$(6 x y) (3 x^{9} y^{6})$ $(6xy)(3x^9y^6)$
$= (6) (x) (y) (3) (x^{9}) (y^{6})$ $=(6)(x)(y)(3)(x^9)(y^6)$

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

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

2 Answers

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