1, power formula: a n = a n- 1 * a, where a is the base and n is the exponent. Root formula: a 1/n = √ a, where a is the base and n is the exponent. Power formula of fractional exponent: a m/n = √ a m/√ a n, where a is the base and m and n are exponents. Negative exponential power formula: a-n = 1/a n n, where a is the base and n is the exponent.

2. power formula: A M N = A Mn, where a is the base and m and n are exponents. Same base powers's division formula: a m/a n = a m-n, where a is the base and m and n are exponents. The exponential formula of zero means: a 0 = 1, where a is the base.

3. negative integer exponential power formula: a-p = 1/a p, where a is the base and p is a positive integer. Positive integer exponential power formula: a p = x p/p! , where a is the radix and p is a positive integer. Binomial theorem formula: a+b n = σ i = 0 ~ ncn, i * a n-i * b i, where a and b are terms and n is an exponent.

Characteristics of power operation

1, exponential power of zero: the power of zero of any non-zero number is 1, for example, 2 0 =1,-3 0 =1and so on. Negative exponential power: the negative n power of any number is equal to the reciprocal of the n power of the number, for example, 2-3 =1/2 3 =1/8,-3-2 =1/3 2 =1/9, etc. Fractional exponential power: the arithmetic of fractional exponential power is, a m/n = sqrta m, a/b m/n = sqrta/b m.

2. Positive integer exponential power: the arithmetic of positive integer exponential power is: a m * a n = a m+na m n = a mn, and the product a/b n = a nb n The arithmetic of negative integer exponential power: negative integer exponential power is: a-m = 1/a m, a/b-n = b/a n, quotient a.

3. Arithmetic of integer exponential power: the distribution law of multiplication, the multiplication law of quotient and the multiplication law of product are all applicable to integer exponential power. Electric power operation is a special operation with its unique operating characteristics. Mastering the laws and characteristics of power operation can help us to do mathematical calculations and better understand mathematical concepts.