Simplify 22^22^2

$2 \cdot 2^{2} \cdot 2^{2}$

Step 1

Multiply $2$ by $2^{2}$ by adding the exponents.

Multiply $2$ by $2^{2}$ .

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

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

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

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

Add $1$ and $2$ .

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

Step 2

Multiply $2^{3}$ by $2^{2}$ by adding the exponents.

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

$2^{3 + 2}$

Add $3$ and $2$ .

$2^{5}$

Step 3

Raise $2$ to the power of $5$ .

$32$

Simplify 2*2^2*2^2