For positive integer n and real number a, the concept of power can be expressed as: n power of a, and recorded as n power of a.
Definition of power
Power refers to a number multiplied by itself n times, where n is a positive integer. For example, the cubic of 2 is expressed as 2 3, that is, 2×2×2=8.
The essence of power
The power supply has the following basic properties:
1.a m× a n = a (m+n): the power multiplied by the same base equals the constant base and exponential addition.
2.(a m) n = a (m× n): power of power, exponential multiplication.
3.(a× b) n = a n× b n: the product of powers is equal to the power of the base and then multiplied.
4.a/m n = (a n) (1/m): the reciprocal of the power is equal to the reciprocal of the base.
5.(a/b) n = (a n)/(b n): the quotient of power equals the quotient of base.
6.A 0 = 1: The power of 0 of any number is equal to 1.
7.A (-n) = 1/(A n): The negative exponent of any number is equal to the positive exponent of its reciprocal.
The use of power
The concept of power is widely used in mathematics and science. The following are some common application scenarios:
1. Calculation expression: Power can be used to calculate power terms in mathematical expressions, such as polynomial expansion and function derivation.
2. Geometric problems: Power can be used to calculate the area and volume of geometric figures, such as squares, circles and spheres.
3. Scientific computing: Power can be used for computing in scientific fields, such as solving problems in physics, chemistry, engineering and other disciplines.
4. Statistical analysis: Power can be used for the calculation of variance and standard deviation in statistics and regression analysis.
5. Financial field: Power can be used to calculate compound interest and interest rate, which is very important for the growth of interest and the estimation of investment return.
The concept of power is expressed by the formula a n, where a is the base and n is the exponent. Power has many properties, including exponential addition with the same base number, multiplication of power and power, and the relationship between power and multiplication.
Power is widely used, including mathematics, science, geometry, statistics and finance. By mastering the concept and related properties of power, we can better understand and apply mathematical knowledge and solve practical problems.