Simplify (2e^x)^2

${(2 e^{x})}^{2}$

Apply the product rule to $2 e^{x}$ .

$2^{2} {(e^{x})}^{2}$

Raise $2$ to the power of $2$ .

$4 {(e^{x})}^{2}$

Multiply the exponents in ${(e^{x})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 e^{x \cdot 2}$

Move $2$ to the left of $x$ .

$4 e^{2 x}$