455 Вправа 455Алгебра 8 клас Бевз 2025 · § 9 · стор. 92

455. Обчисли значення виразу.

а) ${\displaystyle 0,064^2:0,16^3=}$${\displaystyle {(0,4^3)}^2:{(0,4^2)}^3}$=

=${\displaystyle 0,4^6:0,4^6=}$${\displaystyle 0,4^{6-6}=}$${\displaystyle 1}$;

б) ${\displaystyle \frac{{\left(6^6\right)}^2\cdot 36^{-2}}{6^{10}}=}$${\displaystyle \frac{6^{12}\cdot 6^{-4}}{6^{10}}=}$${\displaystyle 6^{12-4-10}=}$${\displaystyle 6^{-2}=}$${\displaystyle \frac{1}{36}}$;

в) ${\displaystyle \frac{0,8^7\cdot 0,16^{-4}}{0,64^3\cdot 0,4^{-7}}=}$${\displaystyle \frac{0,8^7\cdot 0,4^{-8}}{0,8^6\cdot 0,4^{-7}}=}$${\displaystyle 0,8\cdot 0,4^{-1}=}$${\displaystyle \frac{0,8}{0,4}=}$${\displaystyle 2}$;

г) ${\displaystyle {\left(\frac{1}{2}\right)}^2:{\left(\frac{1}{4}\right)}^{-2}\cdot {\left(\frac{1}{2}\right)}^{-7}=}$${\displaystyle {\left(\frac{1}{2}\right)}^2:{\left(\frac{1}{2}\right)}^{-4}\cdot {\left(\frac{1}{2}\right)}^{-7}}$=

=${\displaystyle {\left(\frac{1}{2}\right)}^{2+4-7}=}$${\displaystyle {\left(\frac{1}{2}\right)}^{-1}=}$${\displaystyle 2}$;

ґ) ${\displaystyle {(\frac{1}{2}+\frac{1}{3})}^{-2}:\frac{6}{7}-{\left(1\frac{8}{17}\right)}^{-1}=}$${\displaystyle {\left(\frac{5}{6}\right)}^{-2}\cdot \frac{7}{6}-\frac{17}{25}}$=

=${\displaystyle \frac{36}{25}\cdot \frac{7}{6}-\frac{17}{25}=}$${\displaystyle \frac{42-17}{25}=}$${\displaystyle 1}$.