1. Properties of Exponents
Section 6.1
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6.1 - Exponents

2. 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

3. Definitions
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6.1 - Exponents

4. 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

5. If the BASES are the same, ADD the exponents
Product of a Power
BASE, BASE, ADD
If the BASES are the same, ADD the exponents
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6.1 - Exponents

6. Example 1
Solve 24 • 25
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6.1 - Exponents

7. Example 2
Solve 5x • 5n
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6.1 - Exponents

8. Example 3 Solve 163/4 • 161/4 and leave in exponential form
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6.1 - Exponents

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

10. Power of a Power POWER, POWER, MULTIPLY
If the POWERS are near each other, MULTIPLY the powers – usually deals with PARENTHESES
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6.1 - Exponents

11. Example 4 Solve (23)4 Power, Multiply 12/2/2018 2:19 PM
6.1 - Exponents

12. Example 5
Simplify ((1/2)2)3
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6.1 - Exponents

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

14. Power of a Product
DISTRIBUTE THE POWER TO THE BASES What is/are the base(s) and the power(s)?
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6.1 - Exponents

15. How many bases does this problem have?
Example 6
Simplify (3x)4
How many bases does this problem have?
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6.1 - Exponents

16. Example 7
Simplify (3x2)4
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6.1 - Exponents

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

18. Your Turn
Simplify 𝟏 𝟑 𝒙 𝒚 𝟑 𝟐
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6.1 - Exponents

19. Example 9 Simplify x1/2(x3/4 – x3/2) and leave in exponential form
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6.1 - Exponents

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

21. Negative Power Property
DROP AND SWAP
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6.1 - Exponents

22. Example 10
Simplify (x)–3
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6.1 - Exponents

23. Example 11 Simplify (x y7/4)–2 and leave in exponential form
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6.1 - Exponents

24. Example 12 Simplify (25/36)–1/2 and leave in exponential form
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6.1 - Exponents

25. Quotient Power Property
When dividing an expression with a power, SUBTRACT the powers. The exponent goes with the higher number.
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6.1 - Exponents

26. Example 13
Simplify 𝒙 𝟖 𝒙 𝟑
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6.1 - Exponents

27. Example 14 Simplify −𝟓𝒙 𝟐 𝒚 𝟒 𝟏𝟎𝒙 𝟑 𝒚 𝟐 12/2/2018 2:19 PM
6.1 - Exponents

28. Your Turn Simplify 𝟒 𝟓/𝟐 𝒙 𝟖 𝒚 𝟑 𝟒 𝟏/𝟐 𝒙 𝟏𝟏 𝒚 𝟕 12/2/2018 2:19 PM
6.1 - Exponents

29. 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

30. Example 15
Simplify 𝟐𝒙 𝟑 𝒙 𝟑
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6.1 - Exponents

31. Assignment
Worksheet
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6.1 - Exponents