Question

Сократите дробь 5^n+2*3^2n+7/45^n-3

Answer 1

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