1. Worksheet Key
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6.1 - Exponents

2. Worksheet Key
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3. 11/15/2018 3:32 PM
6.1 - Exponents

4. Properties of Exponents
Section 6.1
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6.1 - Exponents

5. Breakdown of the Exponent
Another way of writing is 251/2.
is written in radical exponent form.
251/2 is written in rational exponent form.
If all possible, convert rational exponent form if possible.
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6.1 - Exponents

6. Breakdown of the Exponent
M is the power (exponent)
N is the root
A is the base
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6.1 - Exponents

7. Example 1
Simplify 43/2
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6.1 - Exponents

8. Example 2
Simplify (–8)4/3
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6.1 - Exponents

9. Your Turn
Simplify –274/3
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6.1 - Exponents

10. Definitions EXPONENT BASE
Base: The term/variable of which is being raised upon
Exponent: The term/variable is raised by a term. AKA Power
EXPONENT
BASE
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6.1 - Exponents

11. Definitions
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6.1 - Exponents

12. Properties of Exponents
Product of a Power:
Power of a Power:
Power of a Product:
Negative Power Property:
Quotient Power Property:
Zero Power Property:
Identity Property:
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6.1 - Exponents

13. If the BASES are the same, ADD the powers
Product of a Power
Saying goes: BASE, BASE, ADD
If the BASES are the same, ADD the powers
What is/are the base(s) and power(s)?
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6.1 - Exponents

14. Example 3
Solve 24 • 25
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6.1 - Exponents

15. Example 4
Simplify 5x • 5n
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6.1 - Exponents

16. Example 5 Solve 163/4 • 161/4 and leave in exponential form
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6.1 - Exponents

17. Your Turn Simplify x • x6/4 and leave in exponential form
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6.1 - Exponents

18. Power of a Power Saying goes: POWER, POWER, MULTIPLY
If the POWERS are near each other, MULTIPLY the powers – usually deals with PARENTHESES
What are the base(s) and the power(s)?
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6.1 - Exponents

19. Example 6 Solve (23)4 Power, Multiply 11/15/2018 3:32 PM
6.1 - Exponents

20. Example 7
Simplify ((1/2)2)3
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6.1 - Exponents

21. Your Turn
Solve [(–2)5]3
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6.1 - Exponents

22. Power of a Product DISTRIBUTE THE POWER TO THE BASES
What is/are the base(s) and the power(s)?
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23. How many bases does this problem have?
Example 8
Simplify (3x)4
How many bases does this problem have?
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6.1 - Exponents

24. Example 9
Simplify (3x2)4
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6.1 - Exponents

25. Example 10 Simplify (8x3/4)2/3 and leave in exponential form
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6.1 - Exponents

26. Your Turn
Simplify
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6.1 - Exponents

27. Example 11 Simplify x1/2(x3/4 – x3/2) and leave in exponential form
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6.1 - Exponents

28. Your Turn Simplify (16x2/5 y4)5/4 and leave in exponential form
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6.1 - Exponents

29. Worksheet Key
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6.1 - Exponents

30. Worksheet Key 2
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6.1 - Exponents

31. 11/15/2018 3:32 PM
6.1 - Exponents

32. Negative Power Property
DROP AND SWAP
What are the base(s) and the power(s)?
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6.1 - Exponents

33. Example 12
Simplify (x)–3
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6.1 - Exponents

34. Example 13 Simplify (x y7/4)–2 and leave in exponential form
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6.1 - Exponents

35. Your Turn Simplify (26 • 46)–1/6 and leave in exponential form
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6.1 - Exponents

36. Example 14 Simplify (25/36)–1/2 and leave in exponential form
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6.1 - Exponents

37. Quotient Power Property
Saying goes: When dividing an expression with a power, SUBTRACT the powers. The exponent goes with the higher number.
What are the base(s) and the power(s)?
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6.1 - Exponents

38. Example 15
Simplify
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6.1 - Exponents

39. Example 16
Simplify
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40. Example 17
Simplify
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41. Your Turn
Simplify
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42. Zero & Identity Power Property
Any base raised to the zero power, besides zero, will always equal to one.
Any bas raised to the first power, besides zero, will always equal to the base.
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6.1 - Exponents

43. Example 18
Simplify
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6.1 - Exponents

44. Your Turn
Solve –30
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6.1 - Exponents

45. Solutions If the exponent is odd If the exponent is even
Exactly one solution for any c
If the exponent is even
When c > 0, there are at least one positive and one negative solution
When c = 0, there are at least one double root solutions
When c < 0, there are at least two imaginary solutions
C. Nth rule: am/n = (n√a)m OR (n√am)
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6.1 - Exponents

46. Example 19
Solve 3x2/3 = 48
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47. 11/15/2018 3:32 PM
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48. Example 20
Solve (x + 2)2/3 + 3 = 7
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49. Your Turn Solve (3x + 43)2/3 + 22 = 38 11/15/2018 3:32 PM
6.1 - Exponents

50. Assignment
Worksheet
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6.1 - Exponents