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Published byAnabel Jennings Modified over 8 years ago
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6.1 PROPERTIES OF EXPONENTS OBJECTIVE: TO SIMPLIFY EXPRESSIONS USING THE PROPERTIES OF EXPONENTS
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DO-NOW Evaluate using your calculator: A. 3 8 B. 3 3 C. 10 5
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DAY 1 PRODUCT OF POWER
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EXPONENT How many times a number is used as a factor
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EXAMPLE:
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LET’S LOOK AT: X 3 X 2
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PRODUCT-OF-POWERS PROPERTY: To multiply powers with the same base, add their exponents. Algebra: a m a n = a n + m Numbers: 5 2 5 4 = 5 6
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EXAMPLES: 2. 2 3 2 4 3. 9 9 4 4. y 2 y 3 5. x n x n + 2
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TRY ON YOUR OWN: A.3 5 3 1 B. Z 6 Z 3 C. a 2 a
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STEPS TO SIMPLIFY: 1. Multiply constants 2. Use product of powers property to simplify variables
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EXAMPLES: 6. (5t)(-30t 2 ) 7. (3x 3 z 2 )(-6y 5 ) 8. (-4a 2 b)(-ac 2 )(3b 2 c 2 )
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TRY ON YOUR OWN: D. (3m 2 )(60mp 2 ) E. (8xz)(-10y)(-2yz 2 )
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HOMEWORK: PRACTICE WORKSHEET!
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DO-NOW: A. B. C.
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DAY 2: POWER OF A POWER (MULTIPLICATION ONLY) COMBINATION OF DAY 1 AND DAY 2
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(X 2 ) 3= LET’S LOOK AT:
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POWER-OF-POWERS PROPERTY: To find a power of a power, multiply the exponents Algebra: (a m ) n = a m n Numbers: (5 2)4 = 5 8
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EXAMPLES: SIMPLIFY 1.2. 3.4.
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(AB) 3= LET’S LOOK AT:
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POWER-OF-POWERS PROPERTY: Algebra: (ab) n = a n b n Numbers: (5 6 ) n = 5 n 6 n
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EXAMPLES: SIMPLIFY 5. 6. 7.
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POWERS OF -1: Even powers: 1 Odd Powers: -1
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EXAMPLES: SIMPLIFY 8. (-1) 5 9. (-t 4 ) 2 10. (-3x) 3
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EXAMPLES: 11. (ab 2 ) 3 (a 3 ) 4 12. (x 5 y 2 ) 3 (xy 8 ) 3
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HOMEWORK: PRACTICE PROBLEMS AT THE BOTTOM OF THE NOTES
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DO-NOW: A. B. C. (-1) 5
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DAY 3 QUOTIENT OF POWERS
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LET’S LOOK AT:
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QUOTIENT-OF- POWERS PROPERTY:
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EXAMPLES: SIMPLIFY 1.2.3.
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EXAMPLES: SIMPLIFY 4.5.6.
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POWERS-OF-A-FRACTION: Algebra:
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EXAMPLES: SIMPLIFY: 7.8.9.
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EXAMPLES: SIMPLIFY: 10.11.
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EXAMPLES: SIMPLIFY: 12.13.
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HOMEWORK: PRACTICE PROBLEMS AT THE BOTTOM OF THE NOTES
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DO-NOW: Use your calculator to find the following:
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DAY 4 – ZEROS NEGATIVES
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ZERO EXPONENTS For any nonzero number a 0 = 1.
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EXAMPLE 1: EVALUATE EACH EXPRESSION a)b) c)d)
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NEGATIVE EXPONENTS: USE YOUR CALCULATOR TO EVALUATE THE FOLLOWING:
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NEGATIVE EXPONENTS: a -n is the reciprocal of a n Algebra: Numbers:
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EXAMPLE 2: REWRITE WITHOUT NEGATIVE EXPONENTS & EVALUATE IF POSSIBLE a)b)c) d)e)
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MIXED REVIEW: REWRITE WITHOUT NEGATIVE OR ZERO EXPONENTS a)b) c)d)
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CLASS WORK: WORK ON 12 PRACTICE PROBLEMS
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DAY 3.5 – PUT IT ALL TOGETHER
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2 ND HALF OF CLASS: WORK ON PRACTICE WS
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