How do you simplify  (9x^5y^4)(3xy^5)4?

Jun 22, 2015

$= 108 {x}^{\textcolor{b l u e}{6}} {y}^{\textcolor{b l u e}{9}}$

Explanation:

$\left(9 {x}^{5} {y}^{4}\right) . \left(3 x {y}^{5}\right) . \left(4\right)$
Rearranging these terms:
$= \left(9 . 3 . 4\right) . \left({x}^{5} . {x}^{1}\right) . \left({y}^{4} . {y}^{5}\right)$

Note: color(blue)(a^m.a^n = a^(m+n)

Applying the above property to the exponents of $x$ and $y$

 = 108. x^color(blue)((5+1)).y^color(blue)((4+5)
$= 108 {x}^{\textcolor{b l u e}{6}} {y}^{\textcolor{b l u e}{9}}$