Evaluate 2^42^5=(22)^(4+5)

$2^{4} \cdot 2^{5} = {(2 \cdot 2)}^{4 + 5}$

Step 1

Multiply $2^{4}$ by $2^{5}$ by adding the exponents.

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

$2^{4 + 5} = {(2 \cdot 2)}^{4 + 5}$

Add $4$ and $5$ .

$2^{9} = {(2 \cdot 2)}^{4 + 5}$

Step 2

Raise $2$ to the power of $9$ .

$512 = {(2 \cdot 2)}^{4 + 5}$

Step 3

Multiply $2$ by $2$ .

$512 = 4^{4 + 5}$

Step 4

Add $4$ and $5$ .

$512 = 4^{9}$

Step 5

Raise $4$ to the power of $9$ .

$512 = 262144$

Evaluate 2^4*2^5=(2*2)^(4+5)