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Теория: Вычисление значения степени-1

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,

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