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Basics about exponents

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Transcript

  • 1. What is an exponent? Exponents are a shorthand way to show a larger number.
  • 2. Where is an exponent located at? Exponents are sometimes referred to as “powers.” Base 6 4 Exponent
  • 3. 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. . . .
  • 4. 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
  • 5. What does an exponent mean? We will use an example of how the secret spread fast to explain what does an exponent mean.
  • 6. 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.
  • 7. • 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!
  • 8. Here is how a secret can spread Round 1 Round 2 Look how many people now know the secret! 3 x 3 = 9 9 people know! I have a secret and I tell 3 of my best friends. My 3 friends each tell 3 more people.
  • 9. 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!) Your BASE = 3 3 4 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.” 3 means 3 x 3 x 3 or 27 4
  • 10. LAWS OF EXPONENTS
  • 11. • 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: a is the BASE and b is the EXPONENT. ab
  • 12. NOTES The laws of exponents show how to SIMPLIFY expressions in exponential form.
  • 13. NOTES In the next few slides, a and b are real numbers and m and n are integers.
  • 14. Product of powers • To multiply powers with the same base, add the exponents. a ∙a = a m n m+n
  • 15. Example: 2 × = 2 2 3 4 3+ 4 =2 7 Proof: 23 × 4 = ( 2 × × ) × 2 × × × ) = 2 2 2 ( 2 2 2 2 × × × × × × =2 2 2 2 2 2 2 7
  • 16. Power of a power • To raise a number in exponential form to a power, multiply the exponents. (a ) = a m n m∙n
  • 17. Example: ( 4 ) = 4 = 4 2 3 3×2 6
  • 18. Power of a product • To find a power of a product, find the power of each factor and multiply. (ab) = a b m m m
  • 19. Example: 36 = 6 = ( 2 ×3) = 2 ×3 2 Proof: 2 ×3 = 4 ×9 = 36 2 2 2 2 2
  • 20. Power of zero • Any nonzero number raised to the power of zero is one. a =1 0
  • 21. Quotient of powers • To find the quotient of powers with the same base, subtract the exponents. a =a n a m m-n
  • 22. •For example… 3 ÷3 =3 2 2 2-2 3 = 3 • 3 =9 =1 2 3 3•3 2 9 =3 0
  • 23. Power of a quotient To raise a quotient to a power, raise both the numerator and denominator to that power. (a/b) = a /b m m m
  • 24. 3 3 2 2 Example:  ÷ = 3 7 7
  • 25. Reciprocals • To change a sign of an exponent, move the expression to the denominator of a fraction, or to the numerator. a = 1/a -n n 1/a = a -n n
  • 26. 1 1 Example #1: 2 = 3 = 2 8 −3 3 1 5 3 Example #2: − 3 = = 5 = 125 5 1
  • 27. 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-f7bd48bf-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-f7bd48bf-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=c977ae81f7bd-48bf-bf86-c88dd4657047&v=default&b=&from_search=11
  • 28. THE END

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