Simplify 2^5*(2^4)^2

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

Step 1

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

$32 \cdot {(2^{4})}^{2}$

Step 2

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

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

$32 \cdot 2^{4 \cdot 2}$

Multiply $4$ by $2$ .

$32 \cdot 2^{8}$

Step 3

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

$32 \cdot 256$

Step 4

Multiply $32$ by $256$ .

$8192$