Повторюємо алгебру за 8 клас: 23

23. Обчисліть, використовуючи властивості степенів:

1) (4^–3)7 • ((4^–2)3)–4 = 4^–21 • 4²⁴ = 4³ = 64;

2) $\frac{{10}^{-5}•({10}^{-7}{)}^4}{{(10}^{-11}{)}^3}$ = $\frac{{10}^{-5}•{10}^{-28}}{{10}^{-33}}$ = $\frac{{10}^{33}}{{10}^5•{10}^{28}}$ = $\frac{{10}^{33}}{{10}^{33}}$ = 1;

3) 4^–5 • ($\frac{1}{2}$)^–8 = (2^2)–5 • 2⁸ = 2^–10 • 2⁸ = 2^–2 = $\frac{1}{2^2}$ = $\frac{1}{4}$ = 0,25;

4) 243^–2 • (3^–7)–2 = (3^{5)–2 •} 3¹⁴ = 3^–10 • 3¹⁴ = 3⁴ = 81;

5) $\frac{{(-5)}^{-4}•{25}^{-2}}{{(-125)}^{-3}}$ = $\frac{{(-125)}^3}{{(-5)}^4•{25}^2}$ = $\frac{{-(5}^3{)}^3}{5^4•(5^2{)}^2}$ = –$\frac{5^9}{5^4•5^4}$ = –$\frac{5^9}{5^8}$ = –5.

6) 0,01^–3 • 10^–8 = (10^–2)–3 • 10^–8 = 10⁶ • 10^–8 = 10^–2 = $\frac{1}{{10}^2}$ = $\frac{1}{100}$ = 0,01.