solve the equation $7^{2} \\cdot 7^{n} = (7^{2})^{4}$ for $n$. $n = \\s…

$solve the equation $7^{2} \\cdot 7^{n} = (7^{2})^{4}$ for $n$. $n = \\s…$

solve the equation $7^{2} \cdot 7^{n} = (7^{2})^{4}$ for $n$.
$n = \square$

$$(7^3)^4 = 7^{3 \times 4} = 7^{12}$$

$$7^2 \cdot 7^n = 7^{2 + n}$$

Since $7^{2+n}=7^{12}$, we get:
$$2 + n = 12$$

$$n = 12 - 2 = 10$$

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