OSSD指数知识

　　指数关系

　　大家好，今天我们来聊一下OSSD11年级初等函数中指数关系的概念。

　　 Introduction:

　　The metric system of measurement is used in most of the world. A key feature of the system is its ease of use. Since all units differ by multiples of 10, it is easy to convert from one unit to another. Consider the chart listing the prefix names and their factors for the unit of measure for length, the metre.

　　世界上大多数国家都采用公制。该系统的一个关键特点是易于使用。因为所有单位都是10的倍数，所以很容易从一个单位转换到另一个单位。考虑一下列出长度度量单位（米）的前缀名称及其因子的图表。

　　In the above chart, we can use the powers to represent metric units lengths that are less than or greater than 1 metre. It will look like the chart below:

　　在上图中，我们可以使用幂来表示小于或大于1米的公制单位长度。如下图所示：

　　2. Definitions:

　　An integer base raised to a negative exponent is equivalent to the reciprocal of the same base raised to the opposite exponent.

　　一个整数基升为负指数，等于同一个基升为相反指数的倒数。

　　where b is not equal to zero.

　　A fractional base raised to a negative exponent is equivalent to the reciprocal of the same base raised to the opposite exponent.

　　分数基数升为负指数等于同一基数升为相反指数的倒数。

　　where a and b are not equal to zero.

　　A number (or expression), other than 0, raised to the power of zero is equal to 1.

　　除0以外的数（或表达式）被提升到零的次幂时等于1。

　　where b is not equal to zero.

　　Working with Rational Exponents：

　　In this learning activity, we will investigate powers involving rational exponents and evaluate expressions containing them.

　　A power involving a rational exponent with numerator 1 and denominator n can be interpreted as the nth root of the base:

　　在这个学习活动中，我们将研究涉及有理指数的幂，并计算包含有理指数的表达式。

　　分子为1分母为n的有理指数的幂可以解释为基数的第n个根：

　　We can evaluate a power involving a rational exponent with numerator m and denominator n by taking the nth root of the base raised to the exponent m:

　　我们可以计算分子m和分母n的有理指数的幂，方法是将基数的第n个根提高到指数m：

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