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

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

Step 1

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

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

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

Multiply $2$ by $3$ .

${(3^{2})}^{6}$

Step 2

Multiply the exponents in ${(3^{2})}^{6}$ .

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

$3^{2 \cdot 6}$

Multiply $2$ by $6$ .

$3^{12}$

Step 3

Raise $3$ to the power of $12$ .

$531441$