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Post1300_section1o4Tu

# Post1300_section1o4Tu - z xy 18 29 29 2 3 2 2 b ab-3...

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1 1.4 Exponents and Radicals Let n be a natural number. Then the exponential expression n x is defined by 43 42 1 times n n x x x x x ..... . . = . n x is read as “ x to the n th power”. Examples: 16 2 . 2 . 2 . 2 2 4 = = , 9 ) 3 )( 3 ( ) 3 ( 2 = - - = - = 3 4 = - 2 ) 5 ( = - 2 5 Rules for Exponents: Multiplying Powers: n m n m a a a + = × Dividing Powers: - = m m n n a a a Negative Powers: 1 - = m m a a and 1 - = n n a a (Note: 0 a ) Power Rule: ( mn n m a a = Zero Power Rule: 0 1 = a If no power is shown, then the exponent is 1. Examples: 1. ( ( 2 3 3 2. ( ( 2 5 4 3 d c d c 3. 2 3 7 9 6 5 c b a c b a 4. ( 29 1 2 3 ) 4 ( 6 12 - - f f e

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2 5. 4 8 - n 6. 2 5 1 - 7. 2 5 - - x x 8. 0 3 2 8 - yz x 9. 5 2 2 3 0 2 36 24 z y x z y x - 10. 1 2 9 3 - xy x 11. 1 5 2 - 12. ( 2 1 0 5 5 2 y y x - - 13. ( 5 4 2 14. ( 3 4 2 5 2 15. ( 2 2 3 5 c b a 16. ( 2 2 5 4 - c b a 17. 2 2 -

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Unformatted text preview: z xy 18. ( 29 ( 29 2 3 2 2 b ab-3 Simplifying Radicals A number y is called the square root of a number x if x y = 2 . (-4) 2 = 4 2 = 16. So, 4 and -4 are both square roots of 16. In general, if x >0, then x has two square roots. However, we use the symbol x for the “principal square root”, which is the positive square root of x . Example: 4 16 = = 25 = 49 Examples: Simplify the following. 1. 64 2. 100 3. 12 4. 50 5. 2 5 6. 3 2 36-Notation: x x = 2 / 1 7. 2 / 1 49 8. 121 100 81 2 / 1 2 / 1-+...
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