Simplify 4^(x+1)*2^(2x)

$4^{x + 1} \cdot 2^{2 x}$

Step 1

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

${(2^{2})}^{x + 1} \cdot 2^{2 x}$

Step 2

Multiply the exponents in ${(2^{2})}^{x + 1}$ .

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

$2^{2 (x + 1)} \cdot 2^{2 x}$

Apply the distributive property.

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

Multiply $2$ by $1$ .

$2^{2 x + 2} \cdot 2^{2 x}$

Step 3

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

$2^{2 x + 2 + 2 x}$

Step 4

Add $2 x$ and $2 x$ .

$2^{4 x + 2}$