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# 指数特性复习

${x}^{n}\cdot {x}^{m}={x}^{n+m}$${2}^{3}\cdot {2}^{5}={2}^{8}$
$\frac{{x}^{n}}{{x}^{m}}={x}^{n-m}$$\frac{{3}^{8}}{{3}^{2}}={3}^{6}$
${\left({x}^{n}\right)}^{m}={x}^{n\cdot m}$${\left({5}^{4}\right)}^{3}={5}^{12}$
$\left(x\cdot y{\right)}^{n}={x}^{n}\cdot {y}^{n}$$\left(3\cdot 5{\right)}^{7}={3}^{7}\cdot {5}^{7}$
${\left(\frac{x}{y}\right)}^{n}=\frac{{x}^{n}}{{y}^{n}}$${\left(\frac{2}{3}\right)}^{5}=\frac{{2}^{5}}{{3}^{5}}$

## 次方的乘积性质

${x}^{n}\cdot {x}^{m}={x}^{n+m}$

### 例题

${5}^{2}\cdot {5}^{5}={5}^{2+5}={5}^{7}$

### 练习

${8}^{6}\cdot {8}^{4}=$

## 次方的除法性质

$\frac{{x}^{n}}{{x}^{m}}={x}^{n-m}$

### 例题

$\frac{{3}^{8}}{{3}^{2}}={3}^{8-2}={3}^{6}$

### 练习

$\frac{{7}^{7}}{{7}^{3}}=$

## 次方的次方性质

${\left({x}^{n}\right)}^{m}={x}^{n\cdot m}$

### 例题

${\left({8}^{2}\right)}^{3}={8}^{2\cdot 3}={8}^{6}$

### 练习

${\left({2}^{4}\right)}^{2}=$

## 乘积的次方值

$\left(x\cdot y{\right)}^{n}={x}^{n}\cdot {y}^{n}$

### 例题

$\left(3\cdot 5{\right)}^{6}={3}^{6}\cdot {5}^{6}$

### 练习

$\left(4\cdot 7{\right)}^{8}=?$

## 分数的次方值

${\left(\frac{x}{y}\right)}^{n}=\frac{{x}^{n}}{{y}^{n}}$

### 例题

${\left(\frac{7}{2}\right)}^{8}=\frac{{7}^{8}}{{2}^{8}}$

### 练习

${\left(\frac{6}{5}\right)}^{9}=?$