Дәреже көрсеткішін табыңыз:
| \(\displaystyle {\displaystyle\frac{4^5\cdot 7^8}{4^3\cdot 7^4}}=(4^5\cdot 7^8):(4^3\cdot 7^4)\,\) | \(\displaystyle =\) | \(\displaystyle \,4\) |
| \(\displaystyle \cdot\) | \(\displaystyle \,7\) |
|
Дәрежелер бөліндісі
\(\displaystyle a\)- нөлдік емес сан, \(\displaystyle n,\, m\) - натурал сандар болсын, ал \(\displaystyle n\ge m\) сонда
\(\displaystyle {\bf \frac{a^{\,n}}{a^{\,m}}}= a^{\,n}:a^{\,m}=a^{\,n\,-\,m}.\)
Формалды азырақ, дәрежелерді бірдей негіздермен бөлген кезде дәреже көрсеткіштері шегеріледі.
\(\displaystyle {\displaystyle\frac{4^5\cdot 7^8}{4^3\cdot 7^4}}=(4^5\cdot 7^8):(4^3\cdot 7^4)=({\color{blue}4}^5\cdot {\color{red}7}^8):({\color{blue}4}^3\cdot {\color{red}7}^4)={\color{blue}4}^{5-3}\cdot {\color{red}7}^{8-4}= {\color{blue}4}^{\bf 2}\cdot {\color{red}7}^{\bf 4}\)
| \(\displaystyle \small{\displaystyle\frac{4^5\cdot 7^8}{4^3\cdot 7^4}}\) | \(\displaystyle \small=(4^5\cdot 7^8):(4^3\cdot 7^4)=({\color{blue}4}^5\cdot {\color{red}7}^8):({\color{blue}4}^3\cdot {\color{red}7}^4)=\) |
\(\displaystyle \small{\displaystyle=\frac{\overbrace{4\cdot 4\cdot 4\cdot 4\cdot 4}^{\bf\color{blue}{5}\text{ рет}}\cdot \overbrace{7\cdot 7\cdot 7\cdot 7\cdot 7\cdot 7\cdot 7\cdot 7}^{\bf\color{red}{8}\text{ рет}}}{\underbrace{4\cdot 4\cdot 4}_{{\bf\color{blue}3}\text{ рет}}\cdot \underbrace{7\cdot 7\cdot 7\cdot 7}_{{\bf\color{red}4}\text{ рет}}}} ={\displaystyle\frac{\overbrace{4\cdot 4\cdot 4\not\cdot 4\not\cdot 4\not}^{\bf(\color{blue}{5}-\color{blue}{3})\text{ рет}}\cdot \overbrace{7\cdot 7\cdot 7\cdot 7\cdot 7\not\cdot 7\not\cdot 7\not\cdot 7\not}^{\bf(\color{red}{8}-\color{red}{4})\text{ рет}}}{4\not\cdot 4\not\cdot 4\not\cdot 7\not\cdot 7\not\cdot 7\not\cdot 7\not}}=\) | |
| \(\displaystyle \small=\overbrace{4\cdot 4}^{\bf\color{blue}{2}\text{ рет}}\cdot \overbrace{7\cdot 7\cdot 7\cdot 7}^{\bf\color{red}{4}\text{ рет}}=\color{blue}{4}^2\cdot \color{red}{7}^4\) |