F.3Maths Laws of indices

1. Simplify (6x-3y)-2(4xy-2)3/(2x3y-2)2 and express the answer in positive indices.

(6x-3y)-2(4xy-2)3/(2x3y-2)2
= (6-2x6y-2)(43x3y-6)/(22x6y4)
= [43/(62•22)]x6+3-6y-2-6-(-4)
= (64/144)x3y-4
= 4x3/9y4


2.Solve the exponential equation 5x+3 - 5x+1 = 24/5 .

5x+3 - 5x+1 = 24/5
52•5x+1 - 5x+1 = 24/5
5x+1(52 - 1) = 24/5
5x+1(25 - 1) = 24/5
5x+1•24 = 24/5
5x+1 = 5-1
x + 1 = -1
x = -2


3Evaluate (28 x 103)2(7 x 105)-1/(20 x 10-2)4,and express the answer in scientific notation.

(28 x 103)2(7 x 105)-1/(20 x 10-2)4
= (282 x 106)(7-1 x 10-5)/(204 x 10-8)
= [282/(7 x 204)] x 106-5-(-8)
= (7 x 10-4) x 109
= 7 x 10-4+9
= 7 x 105


4.Given that n is an integer, simplify (12 x 32n-1 - 2 x 9n)/(9n+1 - 4 x 32n)

(12 x 32n-1 - 2 x 9n)/(9n+1 - 4 x 32n)
= [12 x 32n-1 - 2 x (32)n]/[(32)n+1 - 4 x 32n)
= (12 x 3-1 x 32n - 2 x 32n)/(32 x 32n - 4 x 32n)
= (4 x 32n - 2 x 32n)/(9 x 32n - 4 x 32n)
= (4 - 2)32n/(9 - 4)32n
= 2/5