390. Бөлшектерді қысқартыңдар: 1) (2³·3³·5)/(3²·2³); 2) (45·4²)/(80·3²); 3) (7³·2³)/(16·49); 4) (11·9·5)/(3³·11²); 5) (5²·3³)/(9·25); 6) (5³·29)/(87·25).

Question

Вопрос:

Accepted Answer

Ортақ көбейткіштерді қысқартамыз: \(\frac{2^3\cdot3^3\cdot5}{3^2\cdot2^3}=3\cdot5=15\).
\(45=5\cdot9\), \(4^2=16\), \(80=5\cdot16\): \(\frac{45\cdot4^2}{80\cdot3^2}=\frac{5\cdot9\cdot16}{5\cdot16\cdot9}=1\).
\(16=2^4\), \(49=7^2\): \(\frac{7^3\cdot2^3}{16\cdot49}=\frac{7\cdot2^3}{2^4}=\frac{7}{2}\).
\(9=3^2\): \(\frac{11\cdot9\cdot5}{3^3\cdot11^2}=\frac{5}{3\cdot11}=\frac{5}{33}\).
\(5^2=25\), \(9=3^2\): \(\frac{5^2\cdot3^3}{9\cdot25}=3\).
\(87=3\cdot29\), \(25=5^2\): \(\frac{5^3\cdot29}{87\cdot25}=\frac{5\cdot29}{3\cdot29}=\frac{5}{3}\).

Жауап: 1) 15; 2) 1; 3) \(\frac{7}{2}\); 4) \(\frac{5}{33}\); 5) 3; 6) \(\frac{5}{3}\).

Ответ: