Exponets laws& examples
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This document discusses basic laws and properties of exponents and surds. It begins by defining exponential notation and discussing general cases and special cases of exponents. It then lists several basic laws of exponents, such as am+n = am × an, am/an = am-n, and an-n = a0 = 1. Similar laws are provided for operations involving surds. Examples are provided to illustrate each law. The document also covers simplifying expressions using exponents and surds through factorizing, splitting, and combining like terms. Acknowledgments are provided citing several sources the content was compiled from.
Exponets laws& examples
- 2. Exponential notation represent as Base (real number) to the th power . Exponent Exponent (integers) (integers)
- 3. General case (n is any positive integers) Special cases
- 4. Exponents: Basic laws a .a n = a m 2 .2 3+2 =2 5 =2 = 32 Eg: 3 m+n 2
- 5. Exponents: Basic laws a ÷a n Eg : m = a n–m 3 ÷3 = 3 5–3 2 = 3 = 9 5 3
- 6. Exponents: Basic laws a n–n Eg =a 4 2 4 2 = 24-4 = 20 =1 0 =1
- 7. Exponents: Basic laws (ab) Eg: =a .b n n n 62 =( 2.3) 2 = 22. 32 = 4.9 ∴ 6 = 36 2
- 8. Exponents: Basic laws (a ) m n =a Eg : (23)4 = 2 3x4 = 2 12 mn
- 9. Exponents: Basic laws n a a = n b b Eg: 8 3 n 2 2 8 = 2 3 = 64 9
- 10. Exponents: Basic NB • 2a = a + a = 2 x a • a2 = a . a • ( a + b)2 = a2 + 2ab + b2 ≠ (a2 +b2)
- 11. Exponents an = a . a . a . a ... to n factors a > 0 and a ≠ 1, n ε N a n . a m = a m+n a n ÷ a m = a n–m an – n = a0 = 1 (ab)n = a n . bn (am)n = a mn a b n n a = n b
- 12. Simplify = x x −3 1− x 8 .6 .9 x −1 − x 16 .3 3 x x−3 2 1− x (2 ) .(2.3) .(3 ) 4 x −1 − x (2 ) .3
- 13. 3 x x−3 2 1− x (2 ) .(2.3) .(3 ) 4 x −1 − x (2 ) .3 = 3x x−3 x−3 (2 ) .(2 .3 ).(3 4 x− 4 −x (2 ).(3 ) 2− 2 x )
- 14. x −3 3x x−3 (2 ) .(2 .3 ).(3 4 x− 4 −x (2 ).(3 ) =2 3 x + x − 3− 4 x + 4 = 2 . 3 = /3 2 .3 -1 2− 2 x ) x − 3+ 2 − 2 x + x
- 15. • ie x x −3 1− x 8 .6 .9 x −1 − x 16 .3 = ∴ 3x x−3 (2 ) .(2 .3 ).(3 4 x− 4 −x (2 ).(3 ) =2 3 x + x − 3− 4 x + 4 .3 2 1− x (2 ) .(2.3) .(3 ) 4 x −1 − x ( 2 ) .3 = x −3 x−3 3 x 2− 2 x ) x − 3+ 2 − 2 x + x = 2 . 3 = 2 /3 -1
- 16. 2x 8 =1 2 x −1 16 Solve for x: 3 2x (2 ) =1 4 2 x −1 (2 ) NB 2 =1 0 6x 2 =1 8 x−4 2 2 -2x + 4 = 20 - 2x + 4 = 0 ∴ x =2
- 17. Exponents: solve 3x + 3x -1 = 12 3x + 3x . 3 -1 = 12 3x ( 1 + 3 - 1) = 12 3x ( 1 + 1/3 ) = 12 3x ( 4 / 3 ) = 12 3x 3x ∴ = 12 X ¾ = 32 x = 2
- 18. Surds & Exponents example Basic Laws
- 19. Surds a = a =a 2 3 a 2 =a 2 3 1 2 a≥0 a≥0 18 = 9 . 2 = 3 2
- 20. Surds • NB a . b = a. b • BUT a +b ≠ a+b 2 2 2 2
- 21. Surds • Factors 3 15 125b 4 . 400b = 3 3 15 5 .b 2 1 6 . 4 2 4.2 2. b8 2 2 .2 . 5 . b = 5 64b 8 6 2 4 5.b . 2b . 2 2.5.b 3 2 2 = 7 10b 2 10b 3 .2 2 4 1 2 = b 4
- 22. Surds Simplify: Terms Pure surds Factorise into perfect squares Split Simplify 50 − 18 = 25.2 − 9.2 = 25. 2 − 9 . 2 =5 2 − 3 2 =2 2
- 23. REFERENCE-LIST • This power point presentation is the combination of five power piont presentations, which I gathered on my slide share. However, here below on the next slide are the auther’s I used on my presentation.
- 24. Thank you Guys Acknowledgments to Nurul Atiyah binti Ripin Irma Naziela binti Rosli Stephen Corcoran Genny Simpson http://www.slideshare.net/sibusisot /savedfiles?s_title=exponent-rules-