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

Dec 26, 2016

${e}^{- 2 x + 4} \mathmr{and} {e}^{4 - 2 x}$

#### Explanation:

law of indices:

${a}^{m} \cdot {a}^{n} = {a}^{m + n}$

in the same way:

${e}^{x} \cdot {e}^{y} = {e}^{x + y}$, since the base is the same.

$\therefore {e}^{x} \cdot {e}^{- 3 x} \cdot {e}^{4} = {e}^{x + - 3 x + 4}$

$= {e}^{- 2 x + 4} \mathmr{and} {e}^{4 - 2 x}$