Evaluate (3(2^2)^4)÷2(3(2^3)^4)

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

Step 1

Simplify the numerator.

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

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

$3 \cdot 2^{2 \cdot 4} \div 2 (3 {(2^{3})}^{4})$

Multiply $2$ by $4$ .

$3 \cdot 2^{8} \div 2 (3 {(2^{3})}^{4})$

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

$3 \cdot 256 \div 2 (3 {(2^{3})}^{4})$

Step 2

Simplify the expression.

Multiply $3$ by $256$ .

$768 \div 2 (3 {(2^{3})}^{4})$

Divide $768$ by $2$ .

$384 (3 {(2^{3})}^{4})$

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

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

$384 (3 \cdot 2^{3 \cdot 4})$

Multiply $3$ by $4$ .

$384 (3 \cdot 2^{12})$

Raise $2$ to the power of $12$ .

$384 (3 \cdot 4096)$

Step 3

Multiply $384 (3 \cdot 4096)$ .

Multiply $3$ by $4096$ .

$384 \cdot 12288$

Multiply $384$ by $12288$ .

$4718592$