Operations of construction of number in degree and extraction of a root from it - mathematical operations opposite each other. However they can be combined in one record if to present an exponent of number in a format of a common or decimal fraction. At implementation of the operation which is written down in such a way it is necessary to do consistently both of these mathematical operations.
Instruction
1. If in initial conditions degree it is given in a format of a common fraction, then operation needs to be made in two steps. Their sequence will not affect the received result in any way - begin, for example, with extraction from among a root of that degree which is specified in a fraction denominator. For example, to build in degree ⅔ number 64 on this step it is necessary to take cubic root from it: 64^⅔ = ³ √ 64)² = 4².
2. Build the value received on the first step in the degree equal to the number standing in fraction numerator. The result of this operation will also be result of construction of number in fractional degree. For an example from the previous step completely described course of calculations can be written down so: 64^⅔ = ³ √ 64)² = 4² = 16.
3. You proceed from simplicity of calculations when determining the sequence of the operations of extraction of a root and exponentiation described above. For example, if it was required ⅔ build number 8 in the same degree, then it would be inexpedient to begin with extraction of a cubic root from the eight as the result would be fractional number. In this case it is better to begin with construction 8 in a square, and then to take a cube root from 64 and thus to do without fractional intermediate values: 8^⅔ =³ √ (8²) =³ √ 64 = 4.
4. If the exponent in basic data is given in a format of decimal fraction, then begin with transformation it in a common fraction, and then act on the algorithm described above. For example, for construction of number in degree 0.75 transform this indicator to a common fraction ¾, then take a fourth root and cube the received result.
5. Use any calculator if the course of calculations does not matter, and only the result is important. It can be and the script which is built in Google search engine - with its help is simpler to find the necessary value even, than with use of the Windows OS standard calculator. For example, for construction of number 15 into degree ⅗ pass to the homepage of the website and enter into the field of a search query 15^(3/5). The result of calculations to within 8 signs of Google will display even without pressing of the button of sending inquiry: 15^(3/5) = 5.07755639.