Calculation of fractional degrees generates the difficulties connected with calculations for negative numbers. In this regard, the mathematician for the solution of the tasks connected with fractional degree should remember a number of rules and recommendations.
Instruction
1. Make sure that the task in general has the decision. If the degree basis negative, the mathematics of real numbers forbids construction in fractional degree. In this case it will be necessary to apply complex calculation which is studied by students of the highest technical ulebny institutions.
2. In calculation of fractional degree there is an incident by which , on the one hand, the result of operation −8^1/3 is not determined, but , on the other hand, all know that cubic fractional degrees as you can lose negative roots.
3. If in a task it is required to make calculation of fractional degree of positive number, it is possible to use the calculator with function of exponentiation, for example, the standard Windows calculator. For this purpose enter the degree basis, then press znaok exponentiations, enter an exponent and a nazhnima the Enter key. The result will be removed on the calculator screen.
4. If it is required to solve the equation in which one of arguments is present at fractional degree, the concrete solution depends on a type of this equation. But it is necessary to remember several formulas which help at calculation of fractional degree: A^BC = (A^B) ^CA^(B+C) = A^B · A^Clog(A^B) = B · log(A)
5. When it is necessary to find approximate value of fractional degree of number, and there is no calculator near at hand, use formulas from Paragraph 4. Example: let's find approximate value 100^3/5. 100^3/5 = 10^6/5 = 1000000^1/5 ≈ 1024^1/5 · 1024^1/5 = 4*4 = 16. We check on the calculator: 100^3/5 ≈ 15.85. The value is received by us with a quite good accuracy.