Дәреже көрсеткішін табыңыз:
| \(\displaystyle {\displaystyle\frac{0,01^4\cdot 8,6^5}{0,01^2\cdot 8,6^2}}=(0,01^4\cdot 8,6^5):(0,01^2\cdot 8,6^2)=0,01\) | \(\displaystyle \cdot \,\,8,6\) |
Дәрежелер бөліндісі
\(\displaystyle a\) – нөлдік емес сан, \(\displaystyle n,\, m\) – натурал сандар, және \(\displaystyle n\ge m\) болсын, сонда
\(\displaystyle {\bf \frac{a^{\,n}}{a^{\,m}}}= a^{\,n}:a^{\,m}=a^{\,n\,-\,m}.\)
Ауызша айтқанда, негіздері бірдей дәрежелерді бөлу кезінде дәреже көрсеткіштері шегеріледі.
\(\displaystyle \displaystyle\frac{0,01^4\cdot 8,6^5}{0,01^2\cdot 8,6^2}=(0,01^4\cdot 8,6^5):(0,01^2\cdot 8,6^2)=({\color{blue}{0,01}}^4\cdot {\color{red}{8,6}}^5):({\color{blue}{0,01}}^2\cdot {\color{red}{8,6}}^2)= \)
\(\displaystyle \phantom{\displaystyle\frac{0,01^4\cdot 8,6^5}{0,01^2\cdot 8,6^2}=}={\color{blue}{0,01}}^{4-2}\cdot {\color{red}{8,6}}^{5-2}={\color{blue}{0,01}}^{\bf 2}\cdot {\color{red}{8,6}}^{\bf 3}.\)
| \(\displaystyle {\displaystyle\frac{0,01^4\cdot 8,6^5}{0,01^2\cdot 8,6^2}}\) | \(\displaystyle =(0,01^4\cdot 8,6^5):(0,01^2\cdot 8,6^2)=({\color{blue}{0,01}}^4\cdot {\color{red}{8,6}}^5):({\color{blue}{0,01}}^2\cdot {\color{red}{8,6}}^2)=\) |
\(\displaystyle {\displaystyle=\frac{\overbrace{0,01\cdot 0,01\cdot 0,01\cdot 0,01}^{\bf\color{blue}{4}\text{ рет}}\cdot \overbrace{8,6\cdot 8,6\cdot 8,6\cdot 8,6\cdot 8,6}^{\bf\color{red}{5}\text{ рет}}}{\underbrace{0,01\cdot 0,01}_{{\bf\color{blue}2}\text{ рет}}\cdot \underbrace{8,6\cdot 8,66}_{{\bf\color{red}2}\text{ рет}}}} =\) | |
| \(\displaystyle ={\displaystyle\frac{\overbrace{0,01\cdot 0,01\cdot 0,\rlap{\;/}01\cdot 0,\rlap{\;/}01}^{\bf(\color{blue}{4}-\color{blue}{2})\text{ рет}}\cdot \overbrace{8,6\cdot 8,6\cdot 8,6 \cdot8\rlap{\;/},6\cdot 8\rlap{\;/},6}^{\bf(\color{red}{5}-\color{red}{2})\text{ рет}}}{0,\rlap{\;/}01\cdot 0,\rlap{\;/}01\cdot8\rlap{\;/},6\cdot 8\rlap{\;/},6}}=\) | |
| \(\displaystyle =\overbrace{0,01\cdot 0,01}^{\bf\color{blue}{2}\text{ рет}}\cdot \overbrace{8,6\cdot 8,6\cdot 8,6}^{\bf\color{red}{3}\text{ рет}}=\color{blue}{0,01}^2\cdot \color{red}{8,6}^3.\) |