# How do you multiply 6a ^ -4 (a ^ 5 + 3x ^2 )?

Apr 14, 2015

The Distributive Property of Multiplication tells us that
color(blue)(a*(b+c) = a*b + a*c

$6 {a}^{-} 4 \left({a}^{5} + 3 {x}^{2}\right)$

$= \left(6 {a}^{-} 4 \cdot {a}^{5}\right) + \left(6 {a}^{-} 4\right) \left(3 {x}^{2}\right)$

$= \left\{6 \cdot \left({a}^{-} 4 \cdot {a}^{5}\right)\right\} + \left\{\left(6 \cdot 3\right) \left({a}^{-} 4\right) \left({x}^{2}\right)\right\}$

color(blue)(a^m * a^n = a ^(m+n)

$= \left\{6 \cdot {a}^{- 4 + 5}\right\} + \left\{18 \left({a}^{-} 4\right) \left({x}^{2}\right)\right\}$

$= 6 \cdot a + \left\{18 \left({a}^{-} 4\right) \left({x}^{2}\right)\right\}$

color(green)( = 6*a + 18(x ^2 / a^4)