Suppose we have a rational number a, whose n power is defined as a n, where n is a positive integer. Specifically, a n is to multiply A by N times itself, that is, a× a×...a (* * n A times). For example, 2 3 is 2×2×2, which is 8. We can also define the power of negative numbers. For example, (-2) 3 means (-2)×(-2)×(-2), which is -8.
The power of rational number is not only a mathematical operation, but also has some important properties. The result of power is positive or zero. If a is A Nonnegative rational number, then a n is always nonnegative. Secondly, the power of the power is additive, that is, if both M and N are positive integers, then A (M+N) = A M× A N. In addition, the power of the power is distributable, that is, if C is a rational number, then A (M+N )× C = A M× A N× C.
The power of rational numbers has many applications in mathematics. For example, in algebra, we can use power to calculate the power sum root; In geometry, we can use power to calculate area and volume. The power of rational numbers is also the basis for further study of advanced mathematics, such as advanced numbers, calculus and so on.
Application scenario of rational number power:
1, calculate power sum radical: In algebra, power can be used to calculate power sum radical. For example, we can use power to calculate the power of a number or solve the root of a quadratic equation. Multiplying a number, we can get the multiple of this number or its square, cube, etc. In the fields of science and engineering, power is often used to calculate volume, area, length and so on.
2. Digital coding and encryption: In computer science, power is widely used in digital coding and encryption. For example, RSA algorithm is a power-based encryption algorithm, which uses the characteristics of power operation to encrypt and decrypt information. By multiplying a large prime number, a pair of keys can be generated, thus realizing the encryption and decryption of information.
3. Physics and engineering: In physics and engineering, power also plays an important role. For example, in physics, the calculation of physical quantities such as energy, momentum and charge often involves power operation. In engineering, power operation is used to calculate geometric quantities such as area, volume and length. In materials science, the calculation of strength and hardness of materials often involves power operation.