Question

Сократите дробь 5^n+2*3^2n+7/45^n-3

Answer 1

$frac {5^{n+2}*3^{2n+7}}{45^{n-3}}= frac{5^{n}*5^{2}*3^{2n}*3^{7}}{45^{n}*45^{-3}}= frac{5^{n}*25*9^{n}*2187}{45^{n}* frac{1}{91125} }= frac{45^{n}*25*2187}{45^{n}* frac{1}{91125} } = frac{25*2187}{ frac{1}{91125} } =(25*2187): frac{1}{91125} =25*2187*91125 =5^{2}*3^{7}*5^{3}*3^{3}*3^{3}*=5^{5}*3^{13}$