ГДЗ Алгебра 9 клас Істер НУШ

24. Обчисліть, використовуючи властивості степенів:

1) (5–2)5 • ((5–1)–3)3 = 5–10 • 59 = 5–1 = 1/5 = 0,2;
2) (7^(-4) • (7^(-2) )^5)/(〖(7〗^3 )^(-5) ) = (7^(-4) •7^(-10) )/7^(-15) = 7^15/(7^4 •7^10 ) = 7^15/(7^4 •7^10 ) = 7^15/7^14 = 7;
3) (1/6)–7 • 36–4 = 67 • (62)–4 = 67 • 6–8 = 6–1 = 1/6;
4) 16–5 • (2–3)–7 = (24)–5 • 221 = 2–20 • 221 = 21 = 2;
5) (〖(-3)〗^(-5) •27^(-3) )/〖(-9)〗^(-6) = 〖(-9)〗^6/(〖(-3)〗^5 •27^3 ) = (〖(3〗^2 )^6)/(〖-3〗^5 •〖(3〗^3 )^3 ) = –3^12/(3^5 •3^9 ) = –3^12/3^14 = –1/3^2 = –1/9;
6) 0,2–8 • 25–4 = (1/5)–8 • (52)–4 = 58 • 5–8 = 50 = 1.