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Теория: Преобразование числовых степенных выражений

Задание

Найдите значение числовых выражений:

\(\displaystyle 2^{3}=\),    \(\displaystyle 5^{2}=\),    \(\displaystyle 7^{3}=\)

Решение

Для вычисления значений степеней небольших чисел воспользуемся таблицей степеней (которую желательно знать наизусть).

Информация

Степени числа \(\displaystyle 2:\)

\(\displaystyle \color{blue}{2^{2}}\) \(\displaystyle \color{blue}{2^{3}}\) \(\displaystyle \color{blue}{2^{4}}\) \(\displaystyle \color{blue}{2^{5}}\) \(\displaystyle \color{blue}{2^{6}}\) \(\displaystyle \color{blue}{2^{7}}\) \(\displaystyle \color{blue}{2^{8}}\) \(\displaystyle \color{blue}{2^{9}}\) \(\displaystyle \color{blue}{2^{10}}\)
\(\displaystyle \bf \color{blue}{4}\) \(\displaystyle \bf \color{blue}{8}\) \(\displaystyle \bf \color{blue}{16}\) \(\displaystyle \bf \color{blue}{32}\) \(\displaystyle \bf \color{blue}{64}\) \(\displaystyle \bf \color{blue}{128}\) \(\displaystyle \bf \color{blue}{256}\) \(\displaystyle \bf \color{blue}{512}\) \(\displaystyle \bf \color{blue}{1024}\)

 

Степени числа \(\displaystyle 3:\)

\(\displaystyle \color{green}{3^{2}}\) \(\displaystyle \color{green}{3^{3}}\) \(\displaystyle \color{green}{3^{4}}\) \(\displaystyle \color{green}{3^{5}}\) \(\displaystyle \color{green}{3^{6}}\)
\(\displaystyle \bf \color{green}{9}\) \(\displaystyle \bf \color{green}{27}\) \(\displaystyle \bf \color{green}{81}\) \(\displaystyle \bf \color{green}{243}\) \(\displaystyle \bf \color{green}{729}\)

 

Степени числа \(\displaystyle 4:\)

\(\displaystyle \color{blue}{4^{2}}\) \(\displaystyle \color{blue}{4^{3}}\) \(\displaystyle \color{blue}{4^{4}}\) \(\displaystyle \color{blue}{4^{5}}\)
\(\displaystyle \bf \color{blue}{16}\) \(\displaystyle \bf \color{blue}{64}\) \(\displaystyle \bf \color{blue}{256}\) \(\displaystyle \bf \color{blue}{1024}\)

Степени числа \(\displaystyle 5:\)

\(\displaystyle \color{green}{5^{2}}\) \(\displaystyle \color{green}{5^{3}}\) \(\displaystyle \color{green}{5^{4}}\)
\(\displaystyle \bf \color{green}{25}\) \(\displaystyle \bf \color{green}{125}\) \(\displaystyle \bf \color{green}{625}\)

 

Степени числа \(\displaystyle 6:\)

\(\displaystyle \color{blue}{6^{2}}\) \(\displaystyle \color{blue}{6^{3}}\)
\(\displaystyle \bf \color{blue}{36}\) \(\displaystyle \bf \color{blue}{216}\)

Степени числа \(\displaystyle 7:\)

\(\displaystyle \color{green}{7^{2}}\) \(\displaystyle \color{green}{7^{3}}\)
\(\displaystyle \bf \color{green}{49}\) \(\displaystyle \bf \color{green}{343}\)

Степени числа \(\displaystyle 8:\)

\(\displaystyle \color{blue}{8^{2}}\) \(\displaystyle \color{blue}{8^{3}}\)
\(\displaystyle \bf \color{blue}{64}\) \(\displaystyle \bf \color{blue}{512}\)

Степени числа \(\displaystyle 9:\)

\(\displaystyle \color{green}{9^{2}}\) \(\displaystyle \color{green}{9^{3}}\)
\(\displaystyle \bf \color{green}{81}\) \(\displaystyle \bf \color{green}{729}\)

Таким образом,

\(\displaystyle 2^{3}={\bf 8},\,\, 5^{2}={\bf 25},\,\, 7^{3}={\bf 343}.\)