356 Вправа 356Алгебра 8 клас Тарасенкова 2025 · § 9 · стор. 98

356. Запишіть як степінь з основою 2:

${\displaystyle 4=}$${\displaystyle 2^2}$, ${\displaystyle 8=}$${\displaystyle 2^3}$, ${\displaystyle 16=}$${\displaystyle 2^4}$, ${\displaystyle 32=}$${\displaystyle 2^5}$, ${\displaystyle 64=}$${\displaystyle 2^6}$, ${\displaystyle 0,5=}$${\displaystyle 2^{-1}}$, ${\displaystyle 0,25=}$${\displaystyle 2^{-2}}$.

1) ${\displaystyle 8^{-5}\cdot 4^7=}$${\displaystyle {\left(2^3\right)}^{-5}\cdot {\left(2^2\right)}^7=}$${\displaystyle 2^{-15}\cdot 2^{14}=}$${\displaystyle 2^{-1}}$;

2) ${\displaystyle {64}^5\cdot {16}^{-2}=}$${\displaystyle {\left(2^6\right)}^5\cdot {\left(2^4\right)}^{-2}=}$${\displaystyle 2^{30}\cdot 2^{-8}=}$${\displaystyle 2^{22}}$;

3) ${\displaystyle {\left(2^{-5}\right)}^3\cdot {\left(4^2\right)}^{-3}=}$${\displaystyle 2^{-15}\cdot {\left(2^4\right)}^{-3}=}$${\displaystyle 2^{-15}\cdot 2^{-12}=}$${\displaystyle 2^{-27}}$;

4) ${\displaystyle {\left({16}^5\right)}^9\cdot {\left(8^{-2}\right)}^7=}$${\displaystyle {\left(2^4\right)}^{45}\cdot {\left(2^3\right)}^{-14}=}$${\displaystyle 2^{180}\cdot 2^{-42}=}$${\displaystyle 2^{138}}$;

5) ${\displaystyle {0,5}^{-25}:{\left(4^{-1}\right)}^3=}$${\displaystyle {\left(2^{-1}\right)}^{-25}:{\left(2^{-2}\right)}^3=}$${\displaystyle 2^{25}:2^{-6}=}$${\displaystyle 2^{31}}$;

6) ${\displaystyle {0,25}^{-6}:{32}^{30}=}$${\displaystyle {\left(2^{-2}\right)}^{-6}:{\left(2^5\right)}^{30}=}$${\displaystyle 2^{12}:2^{150}=}$${\displaystyle 2^{-138}}$.