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Section 5.1 Product and Power Rules for Exponents

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5.1 Lecture Guide: Product and Power Rules for Exponents Objective 1: Convert between exponential form and expanded form.

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Algebraically For any natural number n, with base b and exponent n. Verbally For any natural number n, is the product of b used as a ____________ n times. The expression is read as “b to the nth power.” Numerical Example Exponential Notation

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Write each expression in exponential form. 1.2. 3.4.

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Write each exponential expression in expanded form. 5. 6.

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Write each exponential expression in expanded form. 7. 8.

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Write each exponential expression in expanded form. 9. 10.

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11. Complete the warm-up examples below: Expanded Form: Alternate Form:

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Algebraically For any real number x and natural numbers m and n, Verbally To multiply two factors with the same base, use the common base and ____________ the exponents Algebraic Example _________________ Product Rule for Exponents

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12. 13. Simplify Each Expression

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14. 15. Simplify Each Expression

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16. Expanded Form: Alternate form: Objective 3: Use the power rule for exponents. Complete the warm-up examples below:

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Algebraically For any real number x and natural numbers m and n, Verbally To raise a power to a power, ____________ the exponents Algebraic Example _________________ Power Rule for Exponents

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17. 18. Simplify Each Expression

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19. 20. Simplify Each Expression

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21. Expanded Form: Shortcut: Complete the warm-up examples below:

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Algebraically For any real numbers x and y and any natural number, m, Verbally To raise a product to a power, raise each ___________ to this power. To raise a quotient to a power, raise both the ________ and the _________ to this power. Algebraic Example _________________ Raising Products and Quotients to a Power

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22. 23. Simplify Each Expression

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24. 25. Simplify Each Expression

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26. 27. Simplify Each Expression

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28. 29. Simplify Each Expression

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30. Evaluate the expression for and

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Comparing Addition and Multiplication Add the like terms and simplify the products. 31. 32.

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33. 34. Comparing Addition and Multiplication Add the like terms and simplify the products.

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35.36.If possible, addIf possible, multiply Comparing Addition and Multiplication Add the like terms and simplify the products.

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37. The formula for the area of a square is where x is the length of a side of the square. (a) Complete the table of values for the area of a square with sides of length x cm. Length of a side, x cm Area, cm 2 1 2 3 4

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37. The formula for the area of a square is (b) How does the area of a square with sides of length 2 cm compare to the area of a square with sides of length 4 cm? 2 cm 4 cm where x is the length of a side of the square.

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