# How do you simplify (3e^x)(2e^4x)?

Apr 8, 2015

I would try multiplying as:
$3 \cdot 2 {e}^{x} \cdot {e}^{4} \cdot x = 6 x {e}^{x + 4}$

I am not sure you can go beyond this...

Apr 8, 2015

Remember $\left({a}^{m}\right) \cdot \left({a}^{n}\right) = \left({a}^{m + n}\right)$

and $\left(a b\right) \cdot \left(c \mathrm{de}\right)$ can be re-arranged as $\left(a c\right) \cdot \left(b d\right) \cdot \left(e\right)$

Therefore
$\left(3 {e}^{x}\right) \left(2 {e}^{4} x\right)$

$= \left(3 \times 2\right) \left({e}^{x + 4}\right) \left(x\right)$

$= 6 {e}^{x + 4} x$