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六年制重点中学高中数学课本《代数》第三册,第三章中关于指数函数定义如下:y=a~x叫做指数函数,其中a是一个大于零且不等1的常量,函数的定义域是实数集R。关于有理指数幂的概念、性质和运算法则,中学课本已作了详细的论述。至于无理指数幂,课本仅在p_(111)的附脚上注明:a>0,x是一个无理数,a~x是一个确定的实数。其实,当x为无理数时,a~x的具体含意是什么,并不是很直观的,有必要根据目前中学课本所涉及的极限和初等微积分理论,对无理指数幂的概念加以引伸。供同志们参考。
Six years of high school mathematics textbook “Algebra” third book, the third chapter on the definition of the exponential function is as follows: y = a ~ x is called the exponential function, where a is a constant greater than zero and not 1, the definition of the function Domain is a real number set R. On the concept of rational exponentiation of power, nature and algorithms, textbooks have been discussed in detail in secondary schools. As for the unreasonable exponential power, the textbook only states on the foot of p_ (111) that: a> 0, x is an irrational number and a ~ x is a definite real number. In fact, when x is an irrational number, the specific meaning of a ~ x is not very intuitive. It is necessary to extend the concept of irrational exponential power according to the current limit and elementary calculus theory involved in secondary school textbooks. For comrades reference.