Solve for n 2^2*2^n=(2^4)^3

$2^{2} \cdot 2^{n} = {(2^{4})}^{3}$

Step 1

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

$2^{2} \cdot 2^{n} = 2^{4 \cdot 3}$

Step 2

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

$2^{2 + n} = 2^{4 \cdot 3}$

Step 3

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

$2 + n = 4 \cdot 3$

Step 4

Solve for $n$ .

Multiply $4$ by $3$ .

$2 + n = 12$

Move all terms not containing $n$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$n = 12 - 2$

Subtract $2$ from $12$ .

$n = 10$