## 2019年8月30日金曜日

### 数学 - 急速・緩慢に変化する関係 - 指数関数・対数関数 - 指数の拡張 - 指数の拡張(1) - 指数法則、簡約

1. $\begin{array}{l}3-\frac{5}{2}=\frac{1}{2}\\ {a}^{\frac{1}{2}}\end{array}$

2. $\begin{array}{l}\frac{1}{4}+\frac{3}{8}-\frac{1}{2}\\ =\frac{2+3-4}{8}\\ =\frac{1}{8}\\ {a}^{\frac{1}{8}}\end{array}$

3. ${a}^{-5}{b}^{\frac{1}{2}}$

4. $\begin{array}{l}{\left({a}^{\frac{1}{5}}\right)}^{-\frac{5}{2}}\\ ={a}^{-\frac{1}{2}}\end{array}$

5. $\begin{array}{l}\frac{2}{3}·\frac{9}{4}=\frac{3}{2}\\ {a}^{\frac{3}{2}}\end{array}$

6. $\begin{array}{l}{\left({a}^{\frac{1}{3}}{b}^{\frac{8}{3}}{a}^{\frac{5}{2}}{b}^{2}\right)}^{\frac{1}{2}}\\ ={\left({a}^{\frac{17}{6}}{b}^{\frac{14}{3}}\right)}^{\frac{1}{2}}\\ ={a}^{\frac{17}{12}}{b}^{\frac{7}{3}}\end{array}$

7. $\begin{array}{l}{\left({x}^{\frac{1}{2}}\right)}^{2}+2{x}^{\frac{1}{2}}{x}^{-\frac{1}{2}}+{\left({x}^{-\frac{1}{2}}\right)}^{2}\\ =x+2+{x}^{-1}\end{array}$

8. $a-b$

9. $\begin{array}{l}\left({a}^{\frac{1}{2}}-{b}^{\frac{1}{2}}\right)\left({a}^{\frac{1}{2}}+{b}^{\frac{1}{2}}\right)\left(a+b\right)\\ =\left(a-b\right)\left(a+b\right)\\ ={a}^{2}-{b}^{2}\end{array}$