basicsaboutexponents-140308-phpapp01.ppt
- 2. Exponents are a shorthand way to show a larger number. What is an exponent?
- 3. Exponents are sometimes referred to as “powers.” Where is an exponent located at? 6 4 Base Exponent
- 4. How do you read an exponent? A number with an exponent is said to be "raised to the power" of that exponent. Let’s look at some examples. . . .
- 5. 32 = three raised to the second power or three squared 53 = five raised to the third power or five cubed 74 = seven raised to the fourth power
- 6. What does an exponent mean? We will use an example of how the secret spread fast to explain what does an exponent mean.
- 7. How does a secret spread so fast? • The person with a secret tells a friend. • The friend promises never to tell anyone. • That same friend breaks the promise and tells two more friends. • The two new friends tell two new friends.
- 8. • The two new friends decide to tell two more friends. • This pattern occurs over and over until many people have been told. • By the end of the day it is no longer a secret!
- 9. Here is how a secret can spread Round 1 Round 2 I have a secret and I tell 3 of my best friends. My 3 friends each tell 3 more people. Look how many people now know the secret! 3 x 3 = 9 9 people know!
- 10. In an exponential expression, the base is the factor, and the exponent tells the amount of times to multiple that number by itself. (That is a mouthful!) 3 4 Your BASE = 3 Your EXPONENT = 4 • A base is a number that can be expressed using an exponent. • An exponent is the small number and is referred to as a “power.” 34 means 3 x 3 x 3 or 27
- 12. • Recall: A number in exponential form has a base and an exponent. The exponent indicates how many times the base is used as a factor. • In its exponential form: ab a is the BASE and b is the EXPONENT.
- 13. NOTES The laws of exponents show how to SIMPLIFY expressions in exponential form.
- 14. NOTES In the next few slides, a and b are real numbers and m and n are integers.
- 15. Product of powers • To multiply powers with the same base, add the exponents. am ∙an = am+n
- 16. 3 4 3 4 7 Example: 2 2 2 2 3 4 7 Proof: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
- 17. Power of a power • To raise a number in exponential form to a power, multiply the exponents. (am )n = am∙n
- 18. 2 3 3 2 6 Example: 4 4 4
- 19. Power of a product • To find a power of a product, find the power of each factor and multiply. (ab)m = am bm
- 20. 2 2 2 2 2 2 Proof: 2 3 4 9 Example: 36 6 2 3 2 3 36
- 21. Power of zero • Any nonzero number raised to the power of zero is one. a0 = 1
- 22. Quotient of powers • To find the quotient of powers with the same base, subtract the exponents. am = am-n an
- 23. •For example… 32 ÷ 32 = 3 2 - 2 = 30 32 = 3 3 = 9 = 1 32 3 3 9
- 24. Power of a quotient To raise a quotient to a power, raise both the numerator and denominator to that power. (a/b)m = am /bm
- 25. 3 3 3 2 2 Example: 7 7
- 26. Reciprocals • To change a sign of an exponent, move the expression to the denominator of a fraction, or to the numerator. a-n = 1/an 1/a-n = an
- 27. 3 3 1 1 Example #1: 2 2 8 3 3 3 1 5 Example #2: 5 125 5 1
- 28. references Maslijr, 2013, Laws of exponents, viewed 05 March 2014, from http://www.slideshare.net/masljr/laws-of-exponents-23863798 Melnichenko, Y., 2008, Exponents, viewed 05 march 2014, from http://www.slideshare.net/yelena585/exponents-presentation?qid=c977ae81-f7bd- 48bf-bf86-c88dd4657047&v=default&b=&from_search=30 Morris, B., 2012, Grade 6 exponents lesson, viewed 05 March 2014, from http://www.slideshare.net/BobMorris72/math-exponents?qid=c977ae81-f7bd- 48bf-bf86-c88dd4657047&v=default&b=&from_search=2 Scallion, K., 2010, Rules of exponents, viewed 05 March 2014, from http://www.slideshare.net/kscallion/rules-of-exponents Wilkerosn,K., 2013, Exponents, viewed 05 march 2014, from http://www.slideshare.net/katiewilkerosn/exponents-27460394?qid=c977ae81- f7bd-48bf-bf86-c88dd4657047&v=default&b=&from_search=11
- 29. THE END