Найдите показатель степени:
| \(\displaystyle {\displaystyle\frac{0{,}01^4\cdot 8{,}6^5}{0{,}01^2\cdot 8{,}6^2}}=(0{,}01^4\cdot 8{,}6^5):(0{,}01^2\cdot 8{,}6^2)=0{,}01\) | \(\displaystyle \cdot \,\,8{,}6\) |
Частное степеней
Пусть \(\displaystyle a\) – ненулевое число, \(\displaystyle n,\, m\) – натуральные числа, причем \(\displaystyle n\ge m\), 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.
\(\displaystyle \displaystyle\frac{0{,}01^4\cdot 8{,}6^5}{0{,}01^2\cdot 8{,}6^2}=(0{,}01^4\cdot 8{,}6^5):(0{,}01^2\cdot 8{,}6^2)=({\color{blue}{0{,}01}}^4\cdot {\color{red}{8{,}6}}^5):({\color{blue}{0{,}01}}^2\cdot {\color{red}{8{,}6}}^2)= \)
\(\displaystyle \phantom{\displaystyle\frac{0{,}01^4\cdot 8{,}6^5}{0{,}01^2\cdot 8{,}6^2}=}={\color{blue}{0{,}01}}^{4-2}\cdot {\color{red}{8{,}6}}^{5-2}={\color{blue}{0{,}01}}^{\bf 2}\cdot {\color{red}{8{,}6}}^{\bf 3}{\small .}\)
| \(\displaystyle {\displaystyle\frac{0{,}01^4\cdot 8{,}6^5}{0,01^2\cdot 8{,}6^2}}\) | \(\displaystyle =(0{,}01^4\cdot 8{,}6^5):(0,01^2\cdot 8{,}6^2)=({\color{blue}{0{,}01}}^4\cdot {\color{red}{8{,}6}}^5):({\color{blue}{0{,}01}}^2\cdot {\color{red}{8{,}6}}^2)=\) |
\(\displaystyle {\displaystyle=\frac{\overbrace{0{,}01\cdot 0{,}01\cdot 0{,}01\cdot 0{,}01}^{\bf\color{blue}{4}\text{ раза}}\cdot \overbrace{8{,}6\cdot 8{,}6\cdot 8{,}6\cdot 8{,}6\cdot 8{,}6}^{\bf\color{red}{5}\text{ раз}}}{\underbrace{0{,}01\cdot 0{,}01}_{{\bf\color{blue}2}\text{ раза}}\cdot \underbrace{8{,}6\cdot 8{,}6}_{{\bf\color{red}2}\text{ раза}}}} =\) | |
| \(\displaystyle ={\displaystyle\frac{\overbrace{0{,}01\cdot 0{,}01\cdot \cancel {0{,}01}\cdot \cancel {0{,}01}}^{\bf(\color{blue}{4}-\color{blue}{2})\text{ раз}}\cdot \overbrace{8{,}6\cdot 8{,}6\cdot 8{,}6 \cdot \cancel {8{,}6} \cdot \cancel {8{,}6}}^{\bf(\color{red}{5}-\color{red}{2})\text{ раз}}}{ \cancel {0{,}01}\cdot \cancel {0{,}01}\cdot \cancel {8{,}6}\cdot \cancel {8{,}6}}}=\) | |
| |
| \(\displaystyle =\overbrace{0{,}01\cdot 0{,}01}^{\bf\color{blue}{2}\text{ раза}}\cdot \overbrace{8{,}6\cdot 8{,}6\cdot 8{,}6}^{\bf\color{red}{3}\text{ раза}}=\color{blue}{0{,}01}^2\cdot \color{red}{8{,}6}^3.\) |