Question

solve the equation $7^{2} \cdot 7^{n} = (7^{2})^{4}$ for $n$.
$n = $?
$7^{2} \cdot 7^{n} = (7^{2})^{4}$
$7^{2 + n} = 7^{8}$

Explanation:

Step1: Apply exponent product rule

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

Step2: Simplify right-hand side

$(7^{2})^{4} = 7^{2 \times 4} = 7^{8}$

Step3: Equate exponents (same base)

$2 + n = 8$

Step4: Solve for n

$n = 8 - 2 = 6$

Answer:

$6$