276° Вправа 276Алгебра 8 клас Тарасенкова 2025 · § 8 · стор. 83

276. Запишіть числа 0,00001, 1/1000, 0,01, 1/10, 1, 10, 100, 1000, 1 000 000 000 як степінь з основою:

1) Основа 10 (кількість нулів = показник):

${\displaystyle 0,00001=}$${\displaystyle \frac{1}{{10}^5}=}$${\displaystyle {10}^{-5}}$;

${\displaystyle \frac{1}{1000}=}$${\displaystyle {10}^{-3}}$;

${\displaystyle 0,01=}$${\displaystyle {10}^{-2}}$;

${\displaystyle \frac{1}{10}=}$${\displaystyle {10}^{-1}}$;

${\displaystyle 1=}$${\displaystyle {10}^0}$;

${\displaystyle 10=}$${\displaystyle {10}^1}$;

${\displaystyle 100=}$${\displaystyle {10}^2}$;

${\displaystyle 1000=}$${\displaystyle {10}^3}$;

${\displaystyle 1000000000=}$${\displaystyle {10}^9}$.

2) Основа ${\displaystyle \frac{1}{10}}$: ${\displaystyle {10}^n=}$${\displaystyle {\left(\frac{1}{10}\right)}^{-n}}$ — знак показника змінюється:

${\displaystyle 0,00001=}$${\displaystyle {\left(\frac{1}{10}\right)}^5}$;

${\displaystyle \frac{1}{1000}=}$${\displaystyle {\left(\frac{1}{10}\right)}^3}$;

${\displaystyle 0,01=}$${\displaystyle {\left(\frac{1}{10}\right)}^2}$;

${\displaystyle \frac{1}{10}=}$${\displaystyle {\left(\frac{1}{10}\right)}^1}$;

${\displaystyle 1=}$${\displaystyle {\left(\frac{1}{10}\right)}^0}$;

${\displaystyle 10=}$${\displaystyle {\left(\frac{1}{10}\right)}^{-1}}$;

${\displaystyle 100=}$${\displaystyle {\left(\frac{1}{10}\right)}^{-2}}$;

${\displaystyle 1000=}$${\displaystyle {\left(\frac{1}{10}\right)}^{-3}}$;

${\displaystyle 1000000000=}$${\displaystyle {\left(\frac{1}{10}\right)}^{-9}}$.