Question

solve the equation \\(\frac{35^{13}}{35^5} = (35^n)^2\\) for \\(n\\). \\(n = \square\\)

Explanation:

Step1: Simplify left side

$\frac{35^{13}}{35^5}=35^{13-5}=35^8$

Step2: Simplify right side

$(35^n)^2=35^{2n}$

Step3: Equate exponents

$2n=8$

Step4: Solve for n

$n=\frac{8}{2}=4$

Answer:

$4$