Find n identicalfactorproductOfoperation, called the power, also called the power, power, and the result of the power is calledpower(power)。Where, a is calledbase number(base number), n is calledindex(exponent)。When a ⁿ seesThe result of a to the nth power, can also be read as "a to the nth power" or "a to the nth power".
A number can be regarded as its own power, and the index 1 is usually omitted.WritingfractionandnegativeTo the nth power of, parentheses should be added.Four operation sequences: first the square, then the brackets (first the parentheses, then the brackets, and finally the braces), followed by multiplication and division, and addition and subtraction at the end.
Calculate the decimal power of a number. If the decimal is a rational number, convert it into a fraction.In particular, the power of 0 of any number other than 0 is equal to 1.A non positive exponential power of 0 has no meaning.
Isaac NewtonFoundbinomial。Binomials are complex operations in the power.In general, the coefficients of the binomial can also be expressed as follows in the order of arrangement:
one
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
…… …… ……
This is the famousYang Hui Triangle。
Sign rule of rational number power
(1) The even power of a negative number is positive, and the odd power of a negative number is negative.
(2) Any power of a positive number is a positive number.
(3) Any positive power of 0 is 0.
Quick calculation
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The square of some special numbers can speed up the calculation after mastering the rules. Here is an introduction.
The square of a number consisting of n ones
Observe the following example.
1²=1
11²=121
111²=12321
1111²=1234321
11111²=123454321
111111²=12345654321
……
From the above examples, we can see such a rule;Find the square of the number composed of n ones, first write from 1 to n, and then write from n to 1, that is:
11…1(n ones)²=1234…(n-1)n(n-1)…4321
Note: where n only occupies one digit, the full 10 should be carried forward. Of course, suchQuick calculationIt is not advisable to have too many digits.
The square of a number consisting of n 3s
Specific examples:
3²=9
33²=1089
333²=110889
3333²=11108889
33333²=1111088889
It can be seen that:
33…3(n 3)² = 11…11[(n-1) 1]0 88…88[(n-1) 8]nine
One digit is the square of the number of 5
Think of a as the number of 10, soOne digit numberThe square of the number 5 can be written;(10a+5) ².according toPerfect squarededuction;
=
=
=
It can be seen that:One digit number is 5square, equal to the product of the number obtained after removing the single digit number and the number 1 larger than this number,Then write 25.
Pascal language to realize natural number power
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Note: It can only be used to calculate the base number and the exponent are natural numbers, and the power is not greater than 2147483647, otherwise an error will occur
Var a, b, c, i: longint; {The range of longint is large, which is all integers} on [- 21474836482147483647]beginc:=1;{Because all positive integers to the power of 0 are 1}Readln (a, b); {Enter the base number, exponent}If (a=0) and (b=0) then writelin ('Invalid input ');{0 to the power of 0 is meaningless}for i:=1 to b do c:=c*a;{For loop realizes calculation c=a ^ b}writeln(c);{Output c}end.