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Course Properties of Exponents 4-3 Properties of Exponents Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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Course Properties of Exponents Warm Up Evaluate b 2 for b = 4 4. n 2 r for n = 3 and r =

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Course Properties of Exponents Problem of the Day Calculate 6 to the fourth power minus

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Course Properties of Exponents Learn to apply the properties of exponents.

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Course Properties of Exponents The factors of a power, such as 7 4, can be grouped in different ways. Notice the relationship of the exponents in each product = 7 4 (7 7 7) 7 = = 7 4 (7 7) (7 7) = = 7 4

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Course Properties of Exponents

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Course Properties of Exponents Example 1: Multiplying Powers with the Same Base A B. n 5 n 7 n 12 n Add exponents. Multiply. Write the product as one power.

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Course Properties of Exponents D C Think: 2 = 2 1 Example 1: Multiplying Powers with the Same Base Continued Multiply. Write the product as one power. Add exponents.

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Course Properties of Exponents Check It Out: Example 1 A B. x 2 x 3 x 5 x Add exponents. Multiply. Write the product as one power.

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Course Properties of Exponents D C. x 5 y Check It Out: Example 1 Multiply. Write the product as one power. Cannot combine; the bases are not the same. Add exponents. x 5 y 2

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Course Properties of Exponents Notice what occurs when you divide powers with the same base = = 5 5 = 5 2 =

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Course Properties of Exponents Subtract exponents – Example 2: Dividing Powers with the Same Base Divide. Write the quotient as one power. A. x 10 x 9 B. Subtract exponents. x 10 – 9 x Think: x = x 1

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Course Properties of Exponents Subtract exponents – Check It Out: Example 2 Divide. Write the product as one power. A. B. e 10 e 5 Subtract exponents. e 10 – 5 e 5

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Course Properties of Exponents RAISING A POWER TO A POWER Reading Math (9 ) is read as nine to the fourth, to the fifth. 5 4

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Course Properties of Exponents Simplify. Multiply exponents. Example 3: Raising a Power to a Power A. (5 4 ) 2 = = 5 8 B. (6 7 ) 9 = = 6 63 Multiply exponents.

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Course Properties of Exponents Simplify. Example 3: Raising a Power to a Power C. (17 2 ) –20 = 17 2 –20 = 17 –40 Multiply exponents.

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Course Properties of Exponents Simplify. Multiply exponents. Check It Out: Example 3 A. (3 3 ) 4 = = 3 12 B. (4 8 ) 2 = = 4 16 Multiply exponents.

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Course Properties of Exponents Simplify. Check It Out: Example 3 D. (13 4 ) –10 = 13 4 –10 = 13 –40 Multiply exponents.

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Course Properties of Exponents Lesson Quiz Write the product or quotient as one power n 7 1. n 3 n t t 9 t 7 6. (m 2 ) 19 m (9 -8 ) 9 9 –72 8. (10 4 ) 0 1

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