5.8. Теңдікті дәлелдеңдер: 1) (2/3)^5 · (2^5)^3 · 3^7 : (2^10 · 3)^2 = 1; 2) (7^2)^8 · (6^3)^4 : (7^4 · 6^3)^4 = 1; 3) (4/5)^6 · (4^3)^3 · 5^8 : (4^7 · 5)^2 = 4; 4) (9^4 · 8^3)^5 : (9^10)^2 : (8^2)^7 = 8.

Question

Вопрос:

Accepted Answer

Дәрежелер қасиеттерін қолданамыз: \(a^m\cdot a^n=a^{m+n}\), \((a^m)^n=a^{mn}\), \(a^m:a^n=a^{m-n}\).

\(\left(\frac{2}{3}\right)^5\cdot(2^5)^3\cdot3^7:(2^{10}\cdot3)^2=\frac{2^5}{3^5}\cdot2^{15}\cdot3^7: (2^{20}\cdot3^2)=2^{5+15-20}3^{-5+7-2}=1\).
\((7^2)^8\cdot(6^3)^4:(7^4\cdot6^3)^4=7^{16}6^{12}: (7^{16}6^{12})=1\).
\(\left(\frac45\right)^6\cdot(4^3)^3\cdot5^8:(4^7\cdot5)^2=4^{6+9-14}5^{-6+8-2}=4\).
\((9^4\cdot8^3)^5:(9^{10})^2:(8^2)^7=9^{20}8^{15}:9^{20}:8^{14}=8\).

Жауабы: 1) 1; 2) 1; 3) 4; 4) 8.

Ответ: