Simplify ((3^2)^2)^2

${({(3^{2})}^{2})}^{2}$

Multiply the exponents in ${({(3^{2})}^{2})}^{2}$ .

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

${(3^{2})}^{2 \cdot 2}$

Multiply $2$ by $2$ .

${(3^{2})}^{4}$

Multiply the exponents in ${(3^{2})}^{4}$ .

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

$3^{2 \cdot 4}$

Multiply $2$ by $4$ .

$3^{8}$

Raise $3$ to the power of $8$ .

$6561$