10.Mallapragada's. Mathematics / (Surds and Indices-1)

Surds and Indices

Important Facts and Formulae

1.  LAWS OF INDICES:

(i)                         a^m x aⁿ = a^m+n

(ii)                     a^m / aⁿ  = a^m-n 

(iii)                  (a^m)ⁿ     = a^mn

(iv)                  (ab)ⁿ   = aⁿbⁿ

(v)                      (a/b)ⁿ =aⁿ/bⁿ

(vi)                  a^o        = 1

2.  SURDS: Let a be a rational number and n be a positive integer such that a^1/n+ = n_th  root of a

Is called a surd of order n.

3.  LAWS OF SURDS 
 (n_th root of a)^m= n_th root a^m

1.  (243)2/5 =? 2.  (1024)-4/5 =? 3.  {8/125)-4/3=? 4.  (.00032)3/5=? 5.  The value of (256)5/4 6.  The value of (root 8)1/3 7.  The value of {32/243}-4/ 5 8.  The value of {-1/216}-2/3 9.  The value of 51/4X(125)02  5 10.                   1/(243)2/5 + 1/(1024)-4/5+ {8/125)-4/3= 11.                   {2.4 X 103}+{8 X 10-2}=? 12.                   (31/2)5x 92 = 3n x 331/2 13.                   (2n)1/2= 64 Then thevalue of n is : 14.                   (5x51/2 x 53)/5-3/2 = 5x+2 than the value of x 15.                   5n=3125, then the value of 5(n-3)is. 16.                   22n+1 = 1/16n-4, then the valu of n 17.                   (x/y)a-1 = (y/x)a-3then the value of a   Is 18.                   {0(25)7.5x(5)2.5} x 1/(125)1.5 = 57 19.                   (64)-1/2 – (-32)-4/5=? 20.                   The value of ( 8-25-8-26) is pranjali prabha maaths 1.(243)2/5 Ans(35) 2/5   = 32 = 9 2.(1024)-4/5 Ans.(45) )-4/5 =‑4 -4 =  1/ 44  = 1/ 256 3.{8/125)-4/3 Ans. (23/53) )-4/3   = 2-4/5-4 = (5/2) 4 = 625/10 4.(.00032)3/5 Ans.([2/10]5 )3/ 5  (1/5)3 = 1/125 5The value of (256)5/4 Ans.(44) 5/4 = 45 = 1024 6 .The value of (root 8)1/3 Ans. (8 1/3) 1/3 8 1/9 = 7 The value of {32/243}-4/5 Ans. (25 / 35) -4/5  (2/3)-4 = 1/(2/3)4+ (3/2)4           81/16 8. The value of {-1/216}-2/3 Ans. ({-1/6}3) -2/3 = (-1/6)-2  = 1/(1/6)2         1/(1/36) =36 9. The value of 51/4X(125)025 Ans. 51/4X(53)1/4 =5 2.5 x 5 7.5 = 51 =5                     xo=1  10. 1/(243)2/5 + 1/(1024)-4/5+ {8/125)-4/3= Ans. 1/9 + 1/256 + 625/126 11. {2.4 X 103}/{8 X 10-2}=? Ans. 2.4 x 103 / 8 X 10-2            24 x 102 /  8 X 10-2           3 x 10 4 12. (31/2)5x 92 = 3n x 331/2 Ans. 3(5/2+4) = 3 n+3/2              3 13/2  = 3 (2n +3)2          10 = 2n   Therefore  n= 5 13. (2n)1/2= 64 Then the value of n is : Ans. 2 n/2 = 26    n/2 = 6    n= 12 14. (5x51/2 x 53)/5-3/2 = 5x+2 than the value of x Ans. 5(1+1/2+3)/ 5-3/2  = 5 x+2               5(1+1/2+3)+3/2) = 5 x+2          5 12/2 = 5 x+2                5 6 = 5 x+2   theerefore x =4 15. 5n=3125, then the value of 5(n-3)is. Ans.  5(n-3 )  =   5n /53 = 3125/125 = 25 16. 22n+1 = 1/16n-4, then the value of n Ans. 22n+1  =( 24)-n+4          2n + 1 = -4n +16          6n  = 15          2n = 3      There fore n= 3/2    17.(x/y)a-1 = (y/x)a-3then the value of a  is Ans. (x/y)a-1  = ( x/y) –a+3         a-1 = a +3    = 0 18.{(25)7.5x(5)2.5} x 1/(125)1.5 = 5x Ans.(52) 7. 5x (5)2.5/(53) 1.5  =  5x          5 15x (5)2.5/(53) 1.5 =  5x     5 (15 + 2.5 -4.5) = 5x     5 13 = 5x       X  = 13 19.(64)-1/2 – (-32)-4/5=? Ans.( 26) -1/2 = (-25) -4/5             2-3 = (-2)-4 20.The value of ( 8-25-8-26) is Ans. 8-25 (1-8-1)

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