сократить дробь [tex] \frac{45 ^{n+1} }{3 ^{2n+1}*5 ^{n} } } [/tex]. Created by AinurB. algebra-ru

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сократить дробь [tex] \frac{45 ^{n+1} }{3 ^{2n+1}*5 ^{n} } } [/tex]

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ndusha

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$\frac{45 ^{n+1} }{3 ^{2n+1}*5 ^{n} } }= \frac{(5*9) ^{n+1} }{3 ^{2n+1}*5 ^{n} } }= \frac{5^{n+1}*9 ^{n+1} }{3 ^{2n+1}*5 ^{n} } }= \frac{5*9 ^{n+1} }{3 ^{2n+1} } }=\frac{5*(3^2) ^{n+1} }{3 ^{2n+1} } }= \\ =\frac{5*3^{2n+2} }{3 ^{2n+1} } }= 5*3=15$

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