For short record of the work of the same number most on themselves mathematicians thought up a concept of degree. Therefore expression 16*16*16*16*16 can be written down in shorter way. It will have an appearance 16^5. Expression will be read as number 16 in the fifth degree.
It is required to you
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Instruction
1. In a general view the degree registers as a^n. This record means that number a is multiplied by itself by n of times. Expression of a^n is called degree, an is number, basis degrees, n is number, an exponent. For example, a = 4, n = 5, Then we will write down 4^5 = 4*4*4*4*4 = 1,024
2. Degree of n can be negative chislomn =-1,-2,-3, etc. To calculate negative degree of number, it needs to be lowered in a denominator.a^ (-n) = (1/a) ^n = 1/a*1/a*1/a * … * 1/a = 1 / (a^n) we Will consider пример2^(-3) = (1/2) ^3 = 1/2*1/2*1/2 = 1 / (2^3) = 1/8 = 0.125
3. Apparently from an example,-3 degree from number 2 can be calculated in different ways. 1) At first to count fraction 1/2 = 0.5; and then announce in degree 3, i.e. 0.5^3 = 0.5*0.5*0.5 = 0.1252) At first build a denominator in degree 2^3 = 2*2*2 = 8, and then to calculate fraction 1/8 = 0.125.
4. Now we will calculate-1 degree for number, i.e. n =-1. The rules considered above are suitable for this case.a^ (-1) = (1/a) ^1 = 1 / (a^1) = 1/anaprimer, we will build number 5 in-1 степень5^(-1) = (1/5) ^1 = 1 / (5^1) = 1/5 = 0.2.
5. From an example it is visually visible that the number in-1 degree is the return fraction from number. Let's present number 5 in the form of fraction 5/1, then) it is possible not to consider 5^(-1 arithmetically, and at once to write fraction, return 5/1, it is 1/5. So, 15^(-1) = 1/15.6^ (-1) = 1/6.25^ (-1) = 1/25