Simplify ((2^2)^2)^2

${({(2^{2})}^{2})}^{2}$

Step 1

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

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

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

Multiply $2$ by $2$ .

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

Step 2

Multiply the exponents in ${(2^{2})}^{4}$ .

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

$2^{2 \cdot 4}$

Multiply $2$ by $4$ .

$2^{8}$

Step 3

Raise $2$ to the power of $8$ .

$256$