How to build in minus degree

How to build in minus degree

Construction of number in degree is called mathematical operation of consecutive multiplication of this number on itself so many time how many it specifies its degree. It is accepted to call number "basis", and degree - "indicator". Both the basis, and an indicator can be both positive and negative numbers. If with a positive indicator everything is rather clear, then construction of number in negative degree is a little more difficult at calculation.


1. Transform initial record of mathematical operation (construction of number to negative degree) to a form of a common fraction. If to designate the degree basis as X, and the indicator module as a, then record Hzh can be presented in the form of common fraction Hzh/1.

2. Get rid of minus in an exponent. For this purpose it is necessary to trade places numerator and a denominator in the common fraction received on the first step, having left in a fraction indicator (-a) the module of an indicator (a): Hzh = Hzh/1 = 1/Hzh.

3. Find numerical value of the expression standing in a denominator of fraction (Hzh). For example, if the basis of fraction is number 12 (X=12), and the indicator module - number 3 (a=3), then number 1728 (12³=1728) has to be a denominator of fraction. That is the common fraction has to take a form 1/1728.

4. Transfer the fraction received on the previous step from an ordinary form of record to decimal. Most often as a result of such transformation the number with infinite number of signs after a decimal comma (irrational number) turns out therefore the decimal fraction should be rounded to accuracy degree necessary to you. For example, when translating a common fraction in decimal to within seven signs after a comma number 0,0005787 (1/1728≈0,0005787) will turn out 1/1728.

5. Use, for example, computing opportunities of search engines if nobody demands to explain the course of transformations from you. For example, if it is necessary to receive only numerical value of the example used in the previous steps, then there is no need to consistently make all transformations and intermediate calculations 12 ˉ³ = 12 ˉ³/1 = 1/12³ = 1/1728 ≈ 0.0005787. It is enough to pass to the homepage of Google and to enter into the field of a search query 12^(-3). The calculator which is built in search engine will make all necessary transformations and calculations and will show result to within 12 signs after a comma: 12^(-3) ≈ 0.000578703704.

Author: «MirrorInfo» Dream Team