Index Laws Miss Hudson’s Maths

Indices 25 Power (Indice) Base Value Miss Hudson’s Maths

1st Index Law: Multiplication When multiplying terms with the same base we add the powers. Eg 1: y3 x y4 = y7 Eg 2: 23 x 25 = 28 Eg 3: 3 m2 x 2 m3 = 6 m5 Eg 4: c2d5 x 6c5d = 6 c7d6 Miss Hudson’s Maths

2nd Index Law: Division 98 ÷ 95 = 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 = 93 = 93 9 x 9 x 9 x 9 x 9 So although it has a divide sign, when we are dividing indices we actually subtract them. However this can only be done when there is the same base! Miss Hudson’s Maths

When dividing terms with the same base we subtract the powers. eg 1: p 8 ÷ p 2 = p 6 5 5 x4 eg 2: 20x7 ÷ 4x3 1 2 m eg 3: or 3 Miss Hudson’s Maths

3rd Index Law: Power to a further power. You must multiply the powers together, remembering Multiply everything inside the brackets individually. (x2)4 = x8 (-3y)2 = 9y2 (5b3)2 = 25b6 (-2n4)3 = -8n12 Miss Hudson’s Maths

4th Index Law: Power of zero Any term to the power of 0, always equals 1. d0 = 1 40 x 6 = 1 x 6 = 6 50 = 1 132 ÷ 132 = 130 = 1 Miss Hudson’s Maths

Mental Maths: h2 x h3 = h5 d0 = 1 -3 x 4y = -12y 2x 3 2w x 5w2 = 10w3 8z0 x 5z5 = 40z5 4b3 x -2b4 = -8b7 52 x 5 x 50 = 53 (x2)4 = x8 S0 x 42 x s0 = 42 (5b3)2 = 25b6 (-3y)2 = 9y2 (-2n4)3 = -8n12 81x 3 a 2 Miss Hudson’s Maths

5th Index Law: Removing Brackets (Products) (3x4)3 = (3x4) x (3x4) x (3x4) = 3 x 3 x 3 x 4 x 4 x 4 = 33 x 43 (Using the first index law) You must remember that if there is a letter or number by itself, it is to the power of 1. Miss Hudson’s Maths

6th Index Law: Removing Brackets (quotient) = Miss Hudson’s Maths

Four rules for working with powers Revision Miss Hudson’s Maths 25 power index or exponent base 25 = 2 x 2 x 2 x 2 x 2 = 32 Four rules for working with powers Operation Rule Example Multiplying Add powers y5 x y4 = y9 Dividing Subtract powers Powers of Powers Multiply powers Powers of zero Always = 1 ao = 1 Same base

These rules work the same if the base is a number eg: Remember that: am x an = am+n eg y3 x y 4 = y7 eg (am)n = amn eg (y 2)3 = y 6 (ab)m = ambm eg (2y)4 = 16y4 These rules work the same if the base is a number eg: 23 x 22 = 25 42 (32)4 = 38 Miss Hudson’s Maths

7th Index Law: Negative Indices 6-2 = 34 ÷ 39 = = Miss Hudson’s Maths

8th Index Law: Fractional Indices = √36 = Miss Hudson’s Maths

Important numbers to remember: 2 = 21 4 = 22 8 = 23 16 = 24 32 = 25 64 = 26 128 = 27 256 = 28 512 = 29 5 = 51 25 = 52 125 = 53 625 = 54 3125 = 55 3 = 31 9 = 32 27 = 33 81 = 34 243 = 35 Miss Hudson’s Maths