Power of Rational Number Knowledge Point (1) Power of Rational Number
The product of seeking the same factor is called power. The result of power operation is called power. Any power of positive numbers is positive numbers, odd powers of negative numbers are negative numbers, and even powers of negative numbers are positive numbers.
This multiplication of n identical factors A is called power, the result of power is called power, A is called base, and N is called exponent. The 0 th power of any number is 1, for example, 3? = 1
(2) Representation of rational number power
1 same radix power rule
Multiply and divide the power with the same base, the original base is the base, and the sum or difference of indexes is the index.
2. Exponent is a power rule of 0
A 0 = 1, where a≠0, k∈N*
3. Negative integer exponential power rule
A (-k) = 1/(a k), where a≠0, k∈N*
4. Variance:
The sum of two numbers multiplied by the difference between two numbers equals their square difference. (a+b)(a-b)=a^2-b^2
5. Power law
Power, constant radix, exponential multiplication. (a^m)^n=a^(m×n)
6. The efficacy of the product
Product multiplication, first multiply each factor in the product separately, and then multiply the obtained power. (a×b)^n=a^n×b^n
7. exponential power multiplication
The square of the sum (or difference) of two numbers is equal to the sum of their squares plus (or minus) times their product.
(a+b) 2 = a 2+2ab+b 2 or (a-b) 2 = a 2-2ab+b 2.
8. Cubic sum
a^3+b^3=(a+b)(a^2-ab+b^2)
9. polynomial square
(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ac
Addition and subtraction of rational numbers 1. Sign first, then calculate the absolute value.
2. Addition algorithm: the same sign is added, and the absolute value is added. For the addition of different symbols, take the sign of the addend with large absolute value, and subtract the sign with small absolute value from the sign with large absolute value. Two opposite numbers add up to 0. Add and subtract a number with 0, and you still get this number.
3. additive commutative law: a+b=b+a is added, the position of the addend is exchanged, and the sum is unchanged.
4. The law of addition and association: (a+b)+c=a+(b+c) three numbers are added, the first two numbers are added first, or the last two numbers are added first, and the sum is unchanged.
5.a-b=a+(-b) Subtracting a number is equal to adding the reciprocal of this number.