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OBJECTIVE: The students will simplify expressions by using the laws of exponents.

OBJECTIVE: The students will simplify expressions by using the laws of exponents. Write in exponential form 3x3 2x2x2x2x2x2 10x10x10 5x5x5 1x1x1x1x1x1x1x1. HISTORY of the word EXPONENT. The term EXPONENT was introduced by Michael Stifel (1487-1567) in 1544 in Arithmetica integra.

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OBJECTIVE: The students will simplify expressions by using the laws of exponents.

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  1. OBJECTIVE: The students will simplify expressions by using the laws of exponents.

  2. Write in • exponential form • 3x3 • 2x2x2x2x2x2 • 10x10x10 • 5x5x5 • 1x1x1x1x1x1x1x1

  3. HISTORY of the word EXPONENT. • The term EXPONENT was introduced by Michael Stifel (1487-1567) in 1544 in Arithmetica integra.

  4. An exponent is simply shorthand for multiplying that number of identical factors.

  5. So 4³ is the same as (4)(4)(4), three identical factors of 4. And x³ is just three factors of x, (x)(x)(x).

  6. Exponent is the power in an expression. 137 Exponent BASE

  7. Exponents exponent power base

  8. Using the Calculator 5 4 Press 5 Press ^ Press 4 Then =

  9. 7 Laws of Exponents #1PRODUCT LAW • To Multiply LIKE Bases… • …Copy the Base, Add Exponents

  10. Product Law or Product Rule

  11. 7 Laws of Exponents #2QUOTIENT LAW • To Divide LIKE Bases… • …Subtract Exponents a4

  12. Quotient Law or Quotient Rule:

  13. 7 Laws of Exponents #3EXPONENT of EXPONENT LAW • To Raise a Power to a Power… • …Multiply Exponents a12

  14. Exponent of Exponent Law or Exponential Rule:

  15. 7 Laws of Exponents #4Raising a product to a power • To Raise a QUANTITY to a Power, raise EACH Factor to that Power. (-3ab)2= 9a2b2

  16. 7 Laws of Exponents #5Raising a quotient or a fraction to a power • To Raise a FRACTION to a Power, raise BOTH Numerator & Denominator to that power. a4 b4

  17. 7 Laws of Exponents #6NEGATIVE EXPONENT LAW • Negative Exponents  • …Reciprocal with a Positive Exponent 1 a3 ___

  18. #6: Negative Law of Exponents: If the base is powered by the negative exponent, then the base becomes reciprocal with the positive exponent.

  19. 7 Laws of Exponents #7 • Any nonzero number raised to the ZERO Power = ONE 1 1 1

  20. The Laws of Exponents: #7: Zero Law of Exponents: Any base powered by zero exponent equals one

  21. Basic Examples

  22. Basic Examples

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