Question

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^степень
81^n-9^n/3^n+1

Answer 1

$\frac{81^{n} -9^{n} }{3^{n}+1 } =\frac{(3^{n})^{4} -(3^{n)^2} }{3^{n} +1} =\frac{(3^{n})^2((3^{n})^2-1)) }{3^{n}+1 } =\\ \\ \frac{(3^{n})^2*(3^{n} +1)(3^{n}-1) }{3^{n} +1} =(3^{n})^2*(3^{n} -1)=\\ \\ (3^{n})^3-(3^{n})^2 =27^{n} -9^{n}$