456 Вправа 456Алгебра 8 клас Бевз 2025 · § 9 · стор. 92

456. Обчисли значення виразу.

а) ${\displaystyle 0,0081^3\cdot 0,3^{-10}=}$${\displaystyle {(0,3^4)}^3\cdot 0,3^{-10}}$=

=${\displaystyle 0,3^{12}\cdot 0,3^{-10}=}$${\displaystyle 0,3^{12-10}=}$${\displaystyle 0,3^2=}$${\displaystyle 0,09}$;

б) ${\displaystyle \frac{125^5}{25^8\cdot 5^{-3}}=}$${\displaystyle \frac{5^{15}}{5^{16}\cdot 5^{-3}}=}$${\displaystyle 5^{15-16+3}=}$${\displaystyle 5^2=}$${\displaystyle 25}$;

в) ${\displaystyle \frac{9^{-4}\cdot 27^3}{100^5\cdot 10^{-12}}=}$${\displaystyle \frac{3^{-8}\cdot 3^9}{10^{10}\cdot 10^{-12}}=}$${\displaystyle \frac{3}{10^{-2}}=}$${\displaystyle 300}$;

г) ${\displaystyle {\left({\left(\frac{2}{3}\right)}^{-2}\right)}^5:{\left(\frac{2}{3}\right)}^{-9}:\frac{2}{3}=}$${\displaystyle {\left(\frac{2}{3}\right)}^{-10}:{\left(\frac{2}{3}\right)}^{-9}:{\left(\frac{2}{3}\right)}^1}$=

=${\displaystyle {\left(\frac{2}{3}\right)}^{-10+9-1}=}$${\displaystyle {\left(\frac{2}{3}\right)}^{-2}=}$${\displaystyle \frac{9}{4}=}$${\displaystyle 2,25}$;

ґ) ${\displaystyle {(\frac{4}{5}\cdot 4^{-2}+0,2:5^{-2})}^{-1}}$=

=${\displaystyle {(\frac{4}{5}\cdot \frac{1}{16}+0,2\cdot 25)}^{-1}=}$${\displaystyle {(0,05+5)}^{-1}}$=

=${\displaystyle \frac{1}{5,05}=}$${\displaystyle \frac{20}{101}}$.