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Name: _________________________________ Date: ____________________ Period: ______ Properties of Exponents (Exponent is a Whole Number) Notes Warm-Up What is an exponent represent? Explain in your own words. You may show an example to help you explain. Definition of Exponents: a is a real number, n is a natural number a n a a a ... a, n times. Properties of Exponents: Let a and b be nonzero real numbers. Let m and n be integers. Zero Exponent: a0 1 Negative Exponent: an Product: a a Quotient: am a mn an Power of a Power: a a mn Power of a Product: ab a nb n Power of a Quotient: an a bn b m Steps/Reminders *Always look for zero exponents first. You can turn these to 1 and then simplify further as needed. *When doing power of a product or power of a quotient, do not forget to apply the power to any coefficients as well to all variables. *If there is a negative exponent in your answer, then you are not done. Make sure you have flipped all negative exponents. m n n 1 an n a mn n Examples: Use your calculator to solve the following problems. 1. 3 2 5 2 105 2. 8 10 1 Definition: A number is expressed in scientific notation if it is in the form c x 10n where 1 c < 10 and n is an integer. (Example: 3.6 x 105 =36,000 or 8.13 x10-3=0.00813) (Not Examples: 12.6 x10-2 or 0.4 x106) Examples: Solve each of the following Scientific Notation problems. 4.32 x103 3. 4.05 103 3.325 106 4. 6.3x107 Examples: Simplify and write with positive exponents. z9 5. 3 6. k 3 k 5 k 8 z 7. 9a b 2a b 2 3 3b 2 c 5 8. 2 7 cb 5 3 2 10. x5 y 3 9. x 4 x 2 4a b 12. 1 2 a b 3 3 2 3 6 11. a 5 xy bc 2 x 1 13. a x b 4 y c 1 2 y 0 Ticket out the Door What is the hardest thing for you when you are solving these types of problems? 9 s 5t 4 3t 4