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Division with Exponents & Negative and Zero Exponents

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Essential Questions How do I use the division properties of exponents to evaluate powers and simplify expressions? How do I evaluate powers that have negative and zero exponents?

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Activator Simplify 1. (3w 2 ) 2 2. (4vw 3 ) 2 3. (2xy 3 ) 4 (4x 2 y 5 ) Solutions: 1. 9w 4 2. 16v 2 w 6 3. 64x 6 y 17

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Quotient of Powers Property To divide powers having the same base, subtract exponents. Example:

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Power of a Quotient Property To find the power of a quotient, find the power of the numerator and the power of the denominator and then divide. Example:

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Example 1 Simplify completely. 1. 2. = 6 1 = 6 = 4 2 = 16

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Example 2 Simplify completely. 1.2.

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Zero Exponents A nonzero number to the zero power is 1! a 0 = 1, a≠0 Example: 5 0 = 1

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Hmmm…why is that true? Look at the following example: When we subtract exponents we get 4 0 ! So 4 0 = 1

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Negative Exponents Negative exponents must be moved to the denominator! This makes them positive!! Example:

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Example 3 Simplify 1. (-2) 0 = 1 2.

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Example 4 Simplify

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Try This! Simplify

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