ГДЗ Алгебра 9 клас Істер НУШ

23. Обчисліть, використовуючи властивості степенів:

1) (4–3)7 • ((4–2)3)–4 = 4–21 • 424 = 43 = 64;
2) (10^(-5) • (10^(-7) )^4)/(〖(10〗^(-11) )^3 ) = (10^(-5) •10^(-28) )/10^(-33) = 10^33/(10^5 •10^28 ) = 10^33/10^33 = 1;
3) 4–5 • (1/2)–8 = (22)–5 • 28 = 2–10 • 28 = 2–2 = 1/2^2 = 1/4 = 0,25;
4) 243–2 • (3–7)–2 = (35)–2 • 314 = 3–10 • 314 = 34 = 81;
5) (〖(-5)〗^(-4) • 25^(-2))/〖(-125)〗^(-3) = 〖(-125)〗^3/(〖(-5)〗^4•25^2 ) = (〖-(5〗^3 )^3)/(5^4 • (5^2 )^2 ) = –5^9/(5^4 •5^4 ) = –5^9/5^8 = –5.
6) 0,01–3 • 10–8 = (10–2)–3 • 10–8 = 106 • 10–8 = 10–2 = 1/10^2 = 1/100 = 0,01.