1, multiplication of power operation formula same base powers: a m a n = a (m+n). The same base power refers to constant base and exponential addition. For example, the cubic of 2 times the quadratic of 2 equals to the quintic of 2, because the cubic of 2 is 8 and the quadratic of 2 is 4, so 8 times 4 equals 32, that is, the quintic of 2 equals 32.

2. Power of power: (a m) n = a Mn. The power of a power means that the exponent of a power is a power and the base is unchanged. For example, the cubic of 2 times the quadratic of 2 equals to the quintic of 2, because the cubic of 2 is 8 and the quadratic of 2 is 4, so 8 times 4 equals 32, that is, the quintic of 2 equals 32. This formula can be used to quickly calculate and simplify complex mathematical expressions.

3. Division of powers with the same base: a m ÷ a n = a (m-n) (a ≠ 0). Same base powers's division means constant base and exponential subtraction. For example, the third power of 2 divided by the second power of 2 equals to the 1 power of 2, because the third power of 2 is 8 and the second power of 2 is 4, so 8 divided by 4 equals 2, that is, the 1 power of 2 equals 2.

Related knowledge of formulas

1, the formula is widely used. For example, in mathematics, formulas can be used to solve various problems, including algebraic equations, geometric figures, probability statistics and so on. In physics, formulas can be used to describe natural phenomena such as mechanics, electromagnetism and optics. In engineering, the formula can be used to solve various practical problems, including structural design, circuit analysis, fluid dynamics and so on.

2. The characteristic of this formula is that it can simplify complex problems and facilitate calculation and derivation. Each symbol and number in the formula has a specific meaning and function, and the result can be obtained by substituting it into a numerical value or variable. Formulas can also be combined and expanded to form more complex expressions to adapt to different problems and fields.

3. Some problems that should be paid attention to when using the formula. It is necessary to know the applicable scope and restrictive conditions of the formula to ensure that the correct formula is used to solve the corresponding problems. It is necessary to correctly understand and remember the meanings and units of symbols and numbers in the formula to ensure the accuracy and readability of the calculation results. It is necessary to master the derivation methods and skills of formulas in order to calculate and solve problems.