Computing Powers of Positive Integers Using the Modified Detached Coefficients Method and the Staircase Method.

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The Modified Detached Coefficients Method is used to find power numbers ,say Q = (d1d2…dm)n to any positive nth power. The power number is first converted to a multinomial, Say Q= (d1d2d3)3 Q = (d1pm-1 +d2pm-2 +dmp0)n…(1),where m is the number of digits and n is a positive power of the expansion. Then equation (1) is expanded using the multinomial expansion. The coefficients (d’s) of the p’s are extracted to become the result of the power number if and only if all the coefficients are single digits otherwise convert the coefficients which are more than 1 to p’s by replacing 10’s by p. For example, supposing 54 is a coefficient it is replaced by 5p+4,i.e. 5*10+4 =5*p+4. Where 10=p. The Staircase Method is also used to find power numbers. The procedure is the same as the Modified Detached Coefficients Method but after the expansion of the converted form of the power number. The coefficients (d’s) of the p’s are arranged in the staircase form. The result of the power number is then gotten by adding the staircase numbers arrangement column wise as done in multiplication of two numbers. Results of both methods were done manually.
A Thesis presented to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE INDUSTRIAL MATHEMATICS Institute of Distance Learning.June,2013