The meaning of power is somewhat equivalent to continuous multiplication. For example, the power of a number is the product of several numbers. For a simple example, the fifth power of four is the multiplication of five fours, which is 4×4×4×4×4. This is manifested in the form of power: 4? . The 5 in the upper right corner of the tree represents its power, which is called exponent in this number. The bottom 4 is called the bottom. However, there are also some things to pay attention to when expressing. Because we are only exposed to the power whose exponent is a positive integer, we need to pay attention to many things when expressing the power. Such as the power of a negative number, (-4)? Only when brackets are put, it means -4 to the fifth power. But if you say this: -4? This number means the reciprocal of four to the fifth power. So when expressing the power of a number, one thing to remember is to put parentheses to avoid misunderstanding. So how should the multiplier learn its addition, subtraction, multiplication and division?
We can start with the simplest, and try the same base multiplication and division method first. First, multiplication with the same base. Like 10? × 10? . Simple, how to calculate? We have now understood the meaning of power. What is the index? It is the product of several cardinality. So there are two 10 × three 10. It seems that you have to work out how much two tens are multiplied, then how much three tens are multiplied, and then multiply. But it's not that much trouble. Simplify them and you will find 10? × 10? = 10×10×10×10, that is, 5 times10. From this, we can already roughly find the law. In this formula, the cardinal number 10 has not changed, but the indicators are added up. But in order to ensure that 10 is not a special case, we need to try other numbers. 2? ×2? , equal to five twos, so this law holds. In other words, the powers of the same radix are multiplied, the radix remains the same, and the exponents are added.
The next one is to study the power of power, that is to say, how to calculate the power of power. Let's just give an example: (3? )? . As usual, let's simplify it first (3×3×3)? 3×3×3 to the fifth power is equal to five 3×3×3. The simplest one is 3× 3× 3× 3× 3× 3× 3× 3× 3× 3× 3× 3× 3× 3× 3× 3× 3× 3× 3× 3× 3. In fact, it is the third power of 15. At this time, we can find the pattern again. The fifth power of 3 is equal to the third power of 15. Then carefully observe the law, isn't it that the cardinal number remains unchanged and the index doubles? 15 3 times sounds a lot easier? After more experiments, we will find that the power of the same base power is indeed calculated in this way.
? The rest is divided. For example. 10? ÷ 10? = 10? . Five 10 divided by three 10. We already know that multiplication and division are reciprocal and multiplication and division are inverse operations. We can calculate it according to its multiplication operation first. The multiplication operation of this formula is 10 quadratic×10 cubic = 10 quintic. Then at this time we will push them back according to the relationship between strength and weakness. What is the fifth power of 10 divided by the third power of 10? 10 quadratic. Once again, it is concluded that when the cardinality is the same, the calculation is the same, and the exponent of dividend minus the exponent of divisor is equal to the exponent of quotient. This is a division of the same al-Qaeda forces.
But now there is a more intractable problem. What if the exponent of the dividend is less than the exponent of the divisor, that is, the exponent of the final quotient becomes negative? The exponent of quotient becomes negative. What's the negative number? Can this really be worked out? We usually don't see the plural in our life, because giving is smaller than 0. 10.- Two 10? At first I thought it was the reciprocal of 10, but in fact I thought it meant something like this:-10? . So-what exactly does two 10 mean? We can solve it through scientific calculation. In the scientific counting method, there is only one digit before the decimal point, and there is no limit after the decimal point. Then the negative power of 10 is 0. 1. From here we can see how the negative power is calculated. For example, the power of 10 is to move the decimal point to the left by several digits. In addition to power multiplication and division, there are power multiplication and division. However, on the way of learning power addition and subtraction, we will find that they are actually more difficult than multiplication and division. Because the power is equivalent to a multiplication operation, but the multiplication is the same number. Therefore, when calculating the power of multiplication and division, it is equivalent to the same level operation. For example, when calculating same base powers's multiplication and division, you can add their exponents directly. But when you are calculating the addition and subtraction of powers, you can't add up the exponents directly. 10? + 10? , not equal to the fifth power of 10. Because if this formula is simplified, it is the square of 10 plus the cube of 10. 10× 10+ 10× 10× 10。 The calculation result is different from the fifth power of 10.
So let's just say, it's probably the multiplication and division of the same radix power.