Simplify 2(4^k+4^k)

$2 (4^{k} + 4^{k})$

Add $4^{k}$ and $4^{k}$ .

$2 (2 \cdot 4^{k})$

Multiply $2 \cdot 4^{k}$ .

Rewrite $4$ as $2^{2}$ .

$2 (2 \cdot {(2^{2})}^{k})$

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

$2 (2 \cdot 2^{2 k})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 \cdot 2^{1 + 2 k}$

Multiply $2$ by $2^{1 + 2 k}$ by adding the exponents.

Multiply $2$ by $2^{1 + 2 k}$ .

Raise $2$ to the power of $1$ .

$2^{1} \cdot 2^{1 + 2 k}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{1 + 1 + 2 k}$

Add $1$ and $1$ .

$2^{2 + 2 k}$