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Rules of Indices 1. Rules of Indices are on page 21 in the log tables. 2. Always rewrite as a number to a power e.g. 2, 3, 4 etc. etc. 3. Make sure all the base numbers are the same, and on the same level then you can let powers equal each other. e.g.1 e.g.2 52x – 1 = 125 52x – 1 = 53 2x – 1 = 3 2x = 4 X=2 9x = (32) x 27 Rewrite all to the same base and then let power equal each other!! Rule a a 1 2 3 33 = 1 32 32x 32x =3 3 2 1 2 1 2 =3 2x = 2.5 5 X = or 1.25 4 When dividing bases subtract the powers!! Surds ab a . b E.g. 50 25. 2 a a a E.g. 7. 7 7 4 9 E.g. 4 9 or also 5 2 2 3 Treat surds as if they are X’s when adding or subtracting. E.g. also 5 2 3 2 8 2 10 2 4 2 6 2 Rewrite all to same surd so you can add or subtract Surds are multiplied by surds and numbers by numbers. E.g. 3 3 (2 3 3 2 ) 6(3) + 9 ( 6 ) 18 + 9 ( 6 ) Simplifying fractions with surds: If there is a surd in denominator then multiply above and below by surd for it to disappear. E.g. 9 3 9 3 * 3 3 9 3 3 3 3 To solve surds you square everything to get rid of the 3x 10 X E.g.1 ( 3 x 10 ) 2 X 2 3 x 10 X 2 X2-3x-10 = 0 (x+2)(x-5)=0 X=-2 x=5 If you subbed back in it wouldn’t work out for -2. E.g.2 3x 5 x 1 ( 3x 5 ) 2 ( x 1) 2 3x 5 ( x 1)( x 1) 3x 5 x 2 x 1 2 X2 – 5x + 6 = 0 (x – 2) (x – 3) = 0 X=2 X=3 Scientific Notation This involves writing big numbers in index form or scientific notation. E.g. 56,000,000,000,000 is also 5.6 * 1013 Number between 1 and 10 Written as a power of 10 e.g. 260,000 = 2.6 * 105 (move decimal point 5 places to the left) 0.00372 = 3.72 * 10-3 (move decimal place to the right by 3) 1. Addition and Subtraction Write each number as a natural number (positive whole numbers) Add or subtract the numbers Write them in index notation / scientific form E.g.1 5.328 * 105 minus 2.8 * 103 532,800 2,800 530,000 5.3 * 105 E.g.2 6.28 * 10-2 plus 0.0628 plus 0.066 Answer is 6.6*10-2 3.2 * 10-3 0.0032 2. Multiplication and Division Multiply or divide the numbers Multiply or divide the powers of 10 (add or subtract the indices) Write them in index notation / scientific form E.g.1 (6.5 * 103) multiplied by (2.4 * 102) 6.5 * 2.4 = 15.6 15.6 * 105 E.g.2 (3.91*104) (1.7 * 10-1) 3.91 2 .3 1 .7 2.3 * 105 10 4 10 41 10 5 10 1 103 * 102 = 105