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

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

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

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

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

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

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

$2 + n = 3 \cdot 4$

Solve for $n$ .

Multiply $3$ by $4$ .

$2 + n = 12$

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 $12$ .

$n = 10$