Найдите показатель степени:
| \(\displaystyle \frac{(-7{,}3)^{8}}{(-7{,}3)^3}=(-7{,}3)^{8}:(-7{,}3)^3=(-7{,}3)\) |
Частное степеней
Пусть \(\displaystyle a\) – ненулевое число, \(\displaystyle n,\, m\) – натуральные числа, причем \(\displaystyle n\ge m{\small ,}\) тогда
\(\displaystyle {\bf \frac{a^{\,n}}{a^{\,m}}}= a^{\,n}:a^{\,m}=a^{\,n\,-\,m}{\small .}\)
Менее формально, при делении степеней с одинаковыми основаниями показатели степеней вычитаются.
В нашем выражении \(\displaystyle {\displaystyle\frac{(-7{,}3)^{\color{blue}{8}}}{(-7{,}3)^{\color{red}3}}}=(-7{,}3)^{\color{blue}{8}}: (-7{,}3)^{\color{red}3}\):
\(\displaystyle a=(-7{,}3){\small ,}\)
\(\displaystyle n={\color{blue}{8}}\) и \(\displaystyle m={\color{red}3}{\small .}\)
Поэтому
\(\displaystyle {\displaystyle\frac{(-7{,}3)^{\color{blue}{8}}}{(-7{,}3)^{\color{red}3}}}=(-7{,}3)^{\color{blue}{8}}: (-7{,}3)^{\color{red}3}=(-7{,}3)^{\bf {\color{green}{8}-{\color{green}3}}}=(-7{,}3)^{\bf {\color{green}5}}{\small .}\)
Ответ: \(\displaystyle 5{\small .}\)
| \(\displaystyle (-7{,}3)^{\color{blue}{8}}: (-7{,}3)^{\color{red}3}\) | \(\displaystyle \displaystyle=\frac{\overbrace{(-7{,}3)\cdot (-7{,}3)\cdot (-7{,}3)\cdot (-7{,}3)\cdot (-7{,}3)\cdot (-7{,}3)\cdot (-7{,}3)\cdot (-7{,}3) }^ { \bf\color{blue}{8}\text{ раз} } } {\underbrace{ (-7{,}3)\cdot (-7{,}3)\cdot (-7{,}3) }_{ {\bf\color{red}3}\text{ раза}}}=\) |
| \(\displaystyle =\displaystyle\frac{\overbrace{(-7{,}3)\cdot (-7{,}3)\cdot (-7{,}3)\cdot (-7{,}3)\cdot (-7{,}3)\cdot \cancel {(-7{,}3)}\cdot \cancel {(-7{,}3)}\cdot \cancel{(-7{,}3)} }^{ \bf(\color{green}{8-3})\text{ раз} } } {\cancel {(-7{,}3)}\cdot \cancel {(-7{,}3)}\cdot \cancel {(-7{,}3)}}=\) | |
\(\displaystyle = {\underbrace{ {(-7{,}3)\cdot (-7{,}3)\cdot (-7{,}3)\cdot (-7{,}3)\cdot (-7{,}3)}}_{\bf\color{green}{5}\text{ раз}}}=(-7{,}3)^{\bf\color{green}{5}}{\small .}\) |