Sunday, September 11, 2011

Nth power of a number

With the help of binomial theorem we can find out the value of any power of a number.

 We know that

(x+a)^n=∑_(k=0)^n▒〖(n¦k) x^k a^(n-k) 〗

 With the help of above theorem we can calculate the value of any power of a number in following way…

〖11〗^4 =〖(1〗^4) (4 ×1^3×1^1) (6 ×1^2× 1^2) (4 × 1^1×1^3) (1^4)
 = (1) (4) (6) (4) (1)
 = 14641.

〖12〗^(4 ) = (1^(4 ) ) (4× 1^(3 )× 2^(1 ) ) (6×1^(2 )×2^(2 ) ) (4×1^(1 )×2^(3 ) )(2^(4 ) )
 = (1) (8) (24) (32) (16)
 = (1) (8) (24) (32+1) (6)
 = (1) (8) (24+3) (3) (6)
 = (1) (8+2) (7) (3) (6)
 = (1+1) (0) (7) (3) (6)
 = (2) (0) (7) (3) (6)
 = 20736.

〖21〗^(4 ) =〖(2〗^(4 )) (4×2^(3 )×1^(1 ) ) (6×2^(2 )×1^(2 ) ) (4×2^(1 )×1^(3 ) ) (1^(4 ))
= (16) (32) (24) (8) (1)
= (16) (32+2) (4) (8) (1)
= (16) (34) (4) (8) (1)
= (16+3) (4) (4) (8) (1)
= (19) (4) (4) (8) (1)
= 194481.