2017年国家公务员考试行测备考：有理数与分数指数幂教案(2)

第四章指数函数和对数函数

4.1 索引

4.1.1 n 次方根和分数指数幂

教学设计

教学目标

了解 n 次方根和分数指数幂的概念和属性。

掌握分数幂和部首的互化。

教学重点和难点

教学要点

n次方根和分数次幂的概念和性质，分数次幂和根的互化

教学难点

分数幂和根的互化

教学过程

教学链接

教学内容

师生互动

设计意图

1.新课导入

问题：如果 x2=a，那么 a 的 x 是多少？

例如：4的平方根。

老师提出问题，学生回答：x是a的平方根。

引入问题，吸引学生的学习兴趣。

2.探索新知识

如果 x3=a，则 x 称为 a 的立方根。例如：2是8的立方根。

第n个根的定义：一般来说，如果xn=a，那么x称为a的第n个根，其中n>1，n∈N。

n 的值会影响第 n 个根的值吗？小组讨论。

当n为奇数时，正数的n次方根为正数，负数的n次方根为负数。此时a的第n个根用符号表示。

当n为偶数时，正数有两个n次根，且这两个数互为相反数。此时正数a的正n次方根用符号表示，负n次方根用符号表示。

正n次根和负n次根可以组合起来写成(a>0).

负数没有偶数根

问题：为什么负数没有偶数根？

0 的任何根都是 0，记为 =0.

The definition of the radical formula: the formula is called the radical formula, where n is called the root exponent, and a is called the square root. According to the meaning of the nth root, we can get =a.

=A must be true? If it is not true, how to express it?

When n is an odd number, =a

When n is an even number, =|a|=

Complete the textbook P105 example 1

According to the definition of the nth root and the calculation of numbers, we know ==a2=(a>0)

The concept of fractional exponent power: when the exponent of the root exponent (considered as a power) can be divisible by the root exponent, the radical can be expressed in the form of fractional exponent power.

Do you remember the nature of the operations of integer exponential powers.

When the radical is expressed in the form of a fractional exponential power, the operational properties of integer exponential powers are still applicable to fractional exponential powers.

Therefore, it is stipulated that the meaning of a positive fractional exponential power of a positive number is

(a>0,m,n∈N,n>1)

So how to express the exponential power of the negative fraction of a positive number?

We stipulate:

(a>0,m,n∈N,n>1)

The positive fraction exponent power of 0 is equal to 0, and the negative fraction exponential power of 0 is meaningless.

For any rational number r, s, there are the following arithmetic properties:

Complete the textbook P106 cases 2~4

Students discuss the influence of the value of n, strengthen their understanding of the definition of the nth root, and the teacher will correct it after discussing the answer.

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2019-2020 academic year high school mathematics teaching plan a version (2019）必修 first book teaching plan: 4.1.1nth square root and fraction exponent power word version with answers.doc