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Understanding Exponents: Concepts, Definitions, and Applications in Math

Explore the fundamental concept of exponents in mathematics through engaging examples and applications. This content covers the basics of repeated addition, rewriting expressions using exponents, and practical problems involving area and volume where exponents simplify calculations. Learn how to interpret base and exponent, apply laws of exponents, and rewrite numbers in standard and extended forms. Whether you're helping kids share candy or calculating areas, understanding exponents is essential for mastering math!

brett-christensen
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Understanding Exponents: Concepts, Definitions, and Applications in Math

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  1. Daily Dose: There are 3 kids sharing a bag of candy. If the bag of candy is pounds of candy, how much does each kid get? The definition of _________________ is repeated addition. For example, the problem 8 + 8 + 8 + 8 could be rewritten as: _____________ How can you rewrite 8 x 8 x 8 x 8 ? ____________

  2. Exponents!! * My goal is... to use patterns to generate the laws of exponents and apply them. Where is an exponent? What is an exponent? Why do we use exponents?

  3. Location of Exponent • An exponent is a little number high and to the right of a regular number (base number). Exponent 3 4 Base

  4. Definition of Exponent • An exponent tells how many times a number is multiplied by itself. Exponent 3 4 Base = 3 x 3 x 3 x 3 3 4

  5. Why do we use Exponents? • They make things simpler! 7 __ 7 x 7 x 7 =

  6. Why do we use Exponents? • They make things simpler! 7 3 7 x 7 x 7 =

  7. Exponent Language • This exponent is read three to the fourth power. Exponent 3 4 Base

  8. Read These Exponents 3 2 2 3 6 5 7 4

  9. Rewrite using Exponents 2 x 2 x 2 =

  10. Rewrite using Exponents 3 2 x 2 x 2 = 2

  11. Rewrite using Exponents 9 x 9 =

  12. Rewrite using Exponents 2 9 x 9 = 9

  13. Rewrite using Exponents 5 x 5 x 5 x 5 x 5 =

  14. Rewrite using Exponents 5 5 x 5 x 5 x 5 x 5 = 5

  15. Rewrite using Exponents 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 =

  16. Rewrite using Exponents 8 1 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 =

  17. Rewrite using Exponents 8 1 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 = 8 1 =

  18. How to Multiply Out an Exponent to Find theStandard Form (simplify):just multiply, one number at a time. 4 3 = 3 x 3 x 3 x 3 9 27 81

  19. Simplify the Base and Exponentin Standard Form? 2 4 16 =

  20. Simplify the Base and Exponentin Standard Form? 3 2 8 =

  21. Simplify the Base and Exponentin Standard Form? 2 3 9 =

  22. Simplify the Base and Exponentin Standard Form? 0 5 1 =

  23. Daily Dose:1. What is the base number and what is the exponent? 2. What is the value of 9 to the second power? 3. Write in EXTENDED FORM: (written all out): A: B:

  24. Exponents Are Often Used inArea Problems to Show theFeet Are Squared Length x width = area A pool is a rectangle Length = 30 ft. Width = 15 ft. Area = 30 x 15 = 450 ft. 15ft. 30ft 2

  25. Exponents Are Often Used inVolume Problems to Show theCentimeters Are Cubed Length x width x height = volume A box is a rectangle Length = 10 cm. Width = 10 cm. Height = 20 cm. Volume = 20 x 10 x 10 = 2,000 cm. 10 10 10 3

  26. Here Are Some AreasChange Them to Exponents 2 40 feet squared = 40 ft. 56 sq. inches = 56 in. 38 m. squared = 38 m. 56 sq. cm. = 56 cm. 2 2 2

  27. Here Are Some VolumesChange Them to Exponents 3 30 feet cubed = 30 ft. 26 cu. inches = 26 in. 44 m. cubed = 44 m. 56 cu. cm. = 56 cm. 3 3 3

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