EXPONENTS

1. EXPONENTS Product and Quotient of Powers properties

2. What is an exponent? Aquantity representing the power to which a given number or expression is to be raised. Examples:

3. Where do we use them? • Exponents are used to describe a computer’s memory. • 1 gigabyte of RAM (Random Access Memory) means that you have bytes of RAM.

4. Where do we use them? • Exponents are used to measure the strength of Earthquakes(measured in amplitude of ground motion) • Level 1 : • Level 2 : • Level 3 : • In Japan (2004), they had a level 7 Earthquake

5. Where do we use them? • Exponents are used to express large amounts or numbers. • Did you know that a blue whale can eat over krill a day?

6. note taking guide

7. Product of powers property • You can EXPAND expressions to find their PRODUCT. • What do you think is the rule for multiplying POWERS? 4 factors 2 factors a4• a2 = (a • a• a • a) • (a • a) = a4 +2 = a6 6 factors

8. Product of powers property To multiply powers with the same base, add their exponents. Words am• an = am+n Algebra 56• 53 = 59 = 56+3 Numbers

9. practice Product of Powers Property Added Exponents

10. practice Commutative Property of Multiplication Product of Powers Property Added Exponents Simplified *For example: To enter an exponent into your calculator for Select “3” and then select either “^” or “ or “” and then select “5”. Press Enter.

11. 1 1 1 a5 a3 1 1 1 a • a • a • a • a a • a • a a • a • a • a • a a • a • a = = What happens when we divide? What might the answer be and why? 5 factors 2 factors =a • a = a5 –3 = a2 3 factors

12. am an 47 44 Quotient of powers property To divide two powers with the same base, subtract the exponent of the denominator from the exponent of the numerator. Words = am–n Algebra Numbers =47–4 = 43

13. practice Quotient of Powers Property Subtracted Exponents

14. Practice Product of Powers Property Added Exponents Quotient of Powers Property Subtracted Exponents

15. Practice Quotient of Powers Property Subtracted Powers