In primary school, we learned four operations, namely, addition, subtraction, multiplication and division. Then in junior high school, we learned another operation, the fifth operation, that is, the operation of power. What is the operation of power? For example, if 100 is multiplied by ten, then now we don't need to write it in the form of multiplication, and directly write 100 as the power of 100, which is the power operation.

Then the calculation of fate must be inseparable from multiplication, so can power participate in multiplication? This is definitely possible, so we explored the multiplication with the same base. For example, let me give you an example first. Twice of ten times three times of ten. What was his result? First of all, we use the first method to check, that is, write the square of one hundred as 10× 10, then write the cube of ten as 10× 10, and finally multiply them, that is, multiply five tens, so we can write it as the fifth power of ten. You may find that the exponent of their final result is the sum of the two exponents in the original formula, which is the law we found, but now we just give a special case, which needs to be expressed by letters, such as multiplying the m power of ten by the n power of ten. Let's think about his truth, that is, multiply ten m times ten n times, and finally it is the m+N power of ten, then the law we finally get is the multiplication operation with the same base power, and add up the indexes.

However, I realized a problem. Now our cardinality is all ten. If it is any other number, is this rule we found universal? For example, if the square of 1/2 is multiplied by the cube of 1/2, we can also say that two 1/2 are multiplied by three 1/2 and finally multiplied by five 1/2, which is 1/2.

Later, we discussed the power of power and the power of products, for example, (6? )? , how did he calculate? We can continue to decompose, that is, the fourth power of six is quadratic, so it is expressed by formula.

So we divide the square of six into 6×6 and the fourth power of the square of six, that is, there are four such 66% multiplications, so the last eight sixes are multiplying, and we can also regard it as (6×6)? . You may find this index skillfully, which is the product of the dense power and the product power, so we guess whether the law of power sum product power is the product of these two indexes.

If you want it to be universal, you need to express it in letters.

This is the law we found, but what if the radix is not a number, but a formula? For example, (3×5)? When I first saw this formula, I felt that I could multiply each multiplier separately, and then multiply the obtained power, as shown below.

We can decompose this formula again, as shown below.

In this way, we can get our final result. Of course, we also need letters to prove its universality, as shown below.

This is the law we found. To sum up in one sentence, multiply the product multiplier by the product multiplier first, and then multiply it by the power.

At the same time, we also studied the division of power. For example, if the third power of 10 is divided by the second power of 10, I was thinking that multiplication is to add their exponents, so division is not to subtract their exponents. So I tried, the third power of ten, that is, three times ten, and then divided by the second power of ten, that is, divided by two times ten. Finally, it can be written as10×10×10 ÷10, and two can be found.

So we also found same base powers's law of division, which is to subtract their exponents, and the final number is their result, which is expressed in letters as follows.

This is also the operation of power, which is very wonderful and is the fifth operation. Their simplicity is the beauty of simplicity in mathematics.