Generally speaking, in mathematics, we write the product of multiplying n identical factors a as an n [1]. This operation of finding the product of several identical factors is called power, and the result of power is called power. In n, a is called the base and n is called the exponent. N is pronounced "a to the n power" or "a to the n power".

A number can be regarded as the first power of the number itself. For example, 5 is 5 1, and the index 1 is usually omitted. Quadratic is also called square, for example, 5 2 is usually pronounced as "the square of 5"; Cubes are also called cubes. For example, 5 3 can be read as "5 cubes".

express

a^n

Exponential power operation

increase

1. Multiplication with the same radix, radix unchanged, exponential addition.

That is (m, n is a rational number).

2. the power of the power, the base is unchanged, multiplied by the index.

That is (m, n is a rational number).

3. The power of the product is equal to multiplying each factor of the product and then multiplying it by the power.

That is = (m, n is a rational number).

4. Fractional power, numerator power and denominator power.

That is (b≠0). [2]

separate

1. Divide by the same radix power, keep the radix unchanged, and then subtract exponentially.

That is, (a≠0, m and n are rational numbers).

2. Terms:

(1) The zeroth power of any number that is not equal to zero is equal to 1.

That is (a≠0).

(2) The power of -p(p is a positive integer) of any number that is not equal to zero is equal to the reciprocal of the power of p of this number.

That is, (a≠0, p is a positive integer).

(By defining the meaning of zero exponential power and negative integer exponential power, the concept of exponent is extended from positive integer to integer. Various algorithms of exponential power of positive integers are applicable to exponential power of integers. )

Mixed operation

Multiplication and division power mixed operation, first calculate the power, then calculate the multiplication and division; If you encounter parentheses, do the operation in parentheses first.

The operation properties of positive integer exponential power are as follows:

(1) am an = am+n (m, n is a positive integer).

(2)(am)n=amn(m, n is a positive integer)

(3)(ab)n=anbn(n is a positive integer)

4)am÷an=am-n(a≠0, m, n is a positive integer, m >；; n)

(5)a0= 1(a≠0)[3]

pay attention to

When the base of a power is a fraction or a negative number, brackets should be added to the base, such as,.