440 Вправа 440Алгебра 8 клас Бевз 2025 · § 9 · стор. 90

440. Знайди значення виразу.

а) ${\displaystyle 4^{-5}\cdot 4^3=}$${\displaystyle 4^{-5+3}=}$${\displaystyle 4^{-2}=}$${\displaystyle \frac{1}{4^2}=}$${\displaystyle \frac{1}{16}}$;

б) ${\displaystyle 3^6\cdot 3^{-8}=}$${\displaystyle 3^{6-8}=}$${\displaystyle 3^{-2}=}$${\displaystyle \frac{1}{3^2}=}$${\displaystyle \frac{1}{9}}$;

в) ${\displaystyle 0,7^{-6}\cdot 0,7^6=}$${\displaystyle 0,7^{-6+6}=}$${\displaystyle 0,7^0=}$${\displaystyle 1}$;

г) ${\displaystyle {(-6)}^{-8}\cdot {(-6)}^{10}=}$${\displaystyle {(-6)}^{-8+10}}$=

=${\displaystyle {(-6)}^2=}$${\displaystyle 36}$;

ґ) ${\displaystyle {\left(\frac{3}{7}\right)}^{-6}\cdot {\left(\frac{3}{7}\right)}^4=}$${\displaystyle {\left(\frac{3}{7}\right)}^{-6+4}=}$${\displaystyle {\left(\frac{3}{7}\right)}^{-2}=}$${\displaystyle {\left(\frac{7}{3}\right)}^2}$=

=${\displaystyle \frac{49}{9}=}$${\displaystyle 5\frac{4}{9}}$;

д) ${\displaystyle {\left(\frac{1}{3}\right)}^4\cdot {\left(\frac{1}{3}\right)}^{-5}=}$${\displaystyle {\left(\frac{1}{3}\right)}^{4-5}=}$${\displaystyle {\left(\frac{1}{3}\right)}^{-1}=}$${\displaystyle 3}$;

е) ${\displaystyle 8^{-7}\cdot {\left(\frac{1}{8}\right)}^{-8}=}$${\displaystyle 8^{-7}\cdot 8^8=}$${\displaystyle 8^{-7+8}=}$${\displaystyle 8^1=}$${\displaystyle 8}$;

є) ${\displaystyle {\left(\frac{1}{5}\right)}^{-4}\cdot 5^{-2}=}$${\displaystyle 5^4\cdot 5^{-2}=}$${\displaystyle 5^{4-2}=}$${\displaystyle 5^2=}$${\displaystyle 25}$.