Zero Indexes Archives | School Portal NG

Definition of Integer An integer is any positive or negative whole number Example: Simplify the following (+8) + (+3) (ii) (+9) - (+4) Solution (+8) + (+3) +11 (ii) (+9) - (+4) 9-4 +5 or 5 Evaluation Simplify the following (+12) (+7) (ii) 7-(-3)-(-2) Indices The plural of index is indices 10 x 10 x 10 103 in index form, where 3 is the index or power of 10. P5p x pxpxpxp. 5 is the power or index of p in the expression P5. Laws of Indices Multiplication law: ax x ay ax+y E.g. a5xa3a x a x a x a x a x a x a x a a8 y1 x y4y 1+4 y5 a3 x a5 a3 + 5 a8 4c4 x 3c2 4 x 3 x c4 x c2 12 x c4+212c6 Class work Simplify the following (a) 103 x 104 (b) 3 x 106 x 4 x 102 (c) p3 x p (d) 4f3 x 5f7 Division law (1) ax ÷ ay ax ÷ ay ax-y Example Simplify the following a7÷a3a x a x a x a x a x a x a ÷ a x a x a a7-3a4 (2) 106÷103106÷103106-3103 (3) 10a7÷2a210a7÷2a25a7-25a5 Class work Simplify the following 105÷103 2. 51m9÷3m (3) 8x109÷4x106 Zero indexes ax ÷ ax 1 By division law ax-xa0 a01 E.g. 1000 1 5001 Negative index a0 ÷ ax 1/ax But by division law, a0-xa-x Therefore, a-x1/ax Example Simplify (i) b-2 (ii) 2-3 Solution b-2 1/ b2 (ii) 2-3 1/23 1/2x2x2 1/8 Class work (1) 10-2 (2) d0 x d4 x d-2 (3) a-3÷a-5 (4) (1/4)-2 (5) n amxn amn. E.g. 4 x a2 x a2 x a2 a x a x a x a x a x a x a x aa8 Therefore. a2x4a8. (6) am ax na mana. e.g. 242+22xx2 16+4x24 4. 7 Fractional indexes am/n a1/n xmn√ am Example (a1/2)2 a2/2a1a (√a)2√a x √a √a x a√a2ae.g321/55 √321 323/5 5√25x3 23 2x2x2 8 272/33√272 32 3x3x3 9 4-3/2 √1/43 1/23 (0001)3 1x10-3 (10-3)310-3x310-9 1 . 1000000000 0.000000001 (am)p/qamp√(a)p e.g. (162)3/4√ (162)3 (22)3 (4)34x4x4 64 Equator of power for equal base AxAy That is x y WEEKEND ASSIGNMENT Simplify (+13) (+6) (a)7 (b) -7 (c) 19 (d) 8 Simplify (+11) (+6)- (-3) (a)7 (b)8 (c)9 (d)10 Simplify 5x3 x 4x7 (a) 20x4 (b) 20x10 (c) 20x7 (d) 57x10 Simplify 10a8 ÷ 5a6 (a) 2a2 (b) 50a2 (c) 2a14 (d) 2a48 Simplify r7 ÷ r7 (a) 0 (b) 1 (c) r14 (d) 2r7 THEORY Simplify 5y5 x 3y3 24x8 6x Simplify (1/2)-3 See also WEIGHT VOLUME OF CYLINDER AREA OF RIGHT ANGLED TRIANGLE PROFIT AND LOSS PERCENT SIMPLE INTERREST

BASIC OPERATION OF INTEGERS