Solve for d (2^d)^4=2^12

${(2^{d})}^{4} = 2^{12}$

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

$2^{d \cdot 4} = 2^{12}$

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

$d \cdot 4 = 12$

Divide each term in $(d \cdot 4) = 12$ by $4$ and simplify.

Divide each term in $(d \cdot 4) = 12$ by $4$ .

$\frac{(d \cdot 4)}{4} = \frac{12}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{d \cdot 4}{4} = \frac{12}{4}$

Divide $d$ by $1$ .

$d = \frac{12}{4}$

Simplify the right side.

Divide $12$ by $4$ .

$d = 3$