Solve for n (2^4)^2=2^n

${(2^{4})}^{2} = 2^{n}$

Step 1

Rewrite the equation as $2^{n} = {(2^{4})}^{2}$ .

$2^{n} = {(2^{4})}^{2}$

Step 2

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

$2^{n} = 2^{4 \cdot 2}$

Step 3

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$n = 4 \cdot 2$

Step 4

Multiply $4$ by $2$ .

$n = 8$