My own exp nd radi

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Exponential & Radicals KUBHEKA SN
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Transcript of My own exp nd radi

  • 1. Exponential & Radicals KUBHEKA SN

2. Exponential notation represent as to the th power . Exponent (integers) Base (real number) 3. General case (n is any positive integers) Special cases Zero and negative exponent (where a c 0) Example 4. Law of Exponents Law Example 5. Theorem on negative Exponents Prove: Prove: 6. Example : simplifying negative exponents (1) 8 6 682 23242 234 9 3 )()() 3 1 ( ) 3 1 ( x y yx yx yx 7. Principal nth root Where n=positive integer greater than 1 = real number Value for Value for = positive real number b Such that =negative real number b Such that 8. Properties of: RADICAL radicand index Radical sign PROPERTY EXAMPLE 9. Example: combining radicalsQuestion: 12 5 12 5 12 5 3 2 4 1 4 1 3 2 4 1 1 3 2 )( 10. Law of Radicals law example WARNING! 11. Simplifying Radicals Operations with Radicals 12. 2 2 2 2 2 2 1 1 2 4 3 9 4 16 5 25 6 36 1 1 4 2 9 3 16 4 25 5 36 6 2 2 2 2 2 2 7 49 8 64 9 81 10 100 11 121 12 144 49 7 64 8 81 9 100 10 121 11 144 12 13. 2 1) a a b) a2 ba 3) a b b a 14. Simplify: Step 1 Look for Perfect Squares (Try to use the largest perfect square possible.) Step 2 Simplify Perfect Squares Step 3 Multiply the numbers inside and outside the radical separately. 48 3 16 43 4 3 15. Simplify: 48 4 12 34 2 2 3 4 3 16. 2 a a 2 x x Any even power is a perfect square. 4 2 10 5 90 45 x x x x x x The square root exponent is half of the original exponent. 17. Odd powers When you take the square root of an odd power, the result is always an even power and one variable left inside the radical. 5 2 11 5 91 45 x x x x x x x x x 18. Simplifying using variables When you simplify an even power of a variable and the result is an odd power, use absolute value bars to make sure your answer is positive. 14 7 14 12 7 6 x x x y x y Even powers do not need absolute value. 19. Simplify: 3 16x Step 1 Pull out perfect squares Step 2 Simplify 16 2 x x x4 x 4x x 20. a ab b You can only multiply radicals by other radicals 8 3 Both under the radical CAN multiply 8 3 Not under the radical CANNOT multiply 21. What is an nth Root? Extends the concept of square roots. For example: A cube root of 8 is 2, since 23 = 8 A fourth root of 81 is 3, since 34 = 81 For integers n greater than 1, if bn = a then b is an nth root of a. Written where n is the index of the radical. 22. Rational Exponents nth roots can be written using rational exponents. For example: In general, for any integer n greater than 1. 23. Real nth Roots If n is odd: a has one real nth root If n is even: And a > 0, a has two real nth roots And a = 0, a has one nth root, 0 And a < 0, a has no real nth roots 24. Finding nth Roots Find the indicated real nth root(s) of a. Example: n = 3, a = -125 n is odd, so there is one real cube root: (-5)3 = -125 We can write 25. Your Turn! Solve each equation. 5x4 = 80 (x 1)3 = 32 26. http://www.slideshare.net/nurulatiyah/radical-and-exponents- 2?qid=b15cb847-ee58-4b34-aaba- ce8e8ab498a5&v=default&b=&from_search=10 http://www.slideshare.net/holmsted/roots-and-radical- expressions?qid=b15cb847-ee58-4b34-aaba- ce8e8ab498a5&v=default&b=&from_search=12 http://www.slideshare.net/hisema01/71-nth-roots-and-rational- exponents?qid=b15cb847-ee58-4b34-aaba- ce8e8ab498a5&v=default&b=&from_search=15