Transcription of Algebra I Notes Review Properties of Integer Exponents
1 Algebra I Notes Review Properties of Integer Exponents Integer Exponents Review_Notes Page 1 of 13 5/17/2013 In Algebra I, a Review of Properties of Integer Exponents may be required. Students begin their exploration of power under the Common Core in Grade 6 by writing and evaluating expressions with Exponents . In Grade 8, they extend their knowledge of power to Properties of Exponents . Specifically, students should explore, learn, and apply eight Properties of Integer Exponents in the real numbers. Rational Exponents will be addressed later in the course.
2 Know and apply the Properties of Integer Exponents to generate equivalent numerical expressions. Knowledge Targets Students must know Properties of Exponents including: zero exponent , negative exponent , product/quotient of powers, power of power, power of product/quotient. The student will determine the value of exponential expressions using a variety of methods. The student will simplify algebraic expressions by applying the Properties of Exponents . Vocabulary base exponent exponential form power Essential Questions / Big Ideas How can we rewrite and/or simplify expressions in exponential form?
3 Knowing the Properties of Integer Exponents allows us to rewrite expressions in equivalent form. Exponential Expression: consists of a base and an exponent . The exponent tells you how many times to use the base as a factor. a5 = a a a a a (a is used as a factor 5 times) a is the BASE, 5 is the exponent 5a is the 5th POWER of a. Caution: There are some exponential expressions that can be tricky. Ex 1: Power of a Quantity: 3a ba b a b a b 333a bab !!! Ex 2: Power of a Negative Number: 43333381 Mathematical Practices 2.
4 Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Algebra I Notes Review Properties of Integer Exponents Integer Exponents Review_Notes Page 2 of 13 5/17/2013 Ex 3: Negative Power of a Number: 433 3 3 381 Exploration: Ex 4: Simplify the expressions by expanding them first using the definition of an exponent . 1. 23bb 235b bb b b b bb b b b bb 2.
5 42xx 426x xx x x x x xx x x x x xx 3. 2788 2798 88 8 8 8 8 8 8 8 88 8 8 8 8 8 8 8 88 4. 33aa 336a aa a a a a aa a a a a aa using the pattern that emerged from the examples above, have students write a rule for multiplying exponential expressions. Product of Powers Property: To multiply powers with the same base, add the Exponents . Ex 5: Simplify the expressions using the product of powers property.
6 1. 23bb 232 35b bbb 2. 42xx 424 26x xxx 3. 2788 272 798 888 4. 33aa 333 36a aaa Exploration: Ex 6: Simplify the expressions by expanding them first using the definition of an exponent . 1. 32y 322222 2 26yyyyyy 2. 254 25555 51044444 3. 43x 4333333 3 3 312xxxxxxx using the pattern that emerged from the examples above, have students write a rule for raising an exponential expression to a power. Algebra I Notes Review Properties of Integer Exponents Integer Exponents Review_Notes Page 3 of 13 5/17/2013 Power of a Power Property: To find a power of a power, multiply the Exponents .
7 Ex 7: Simplify the expressions using the power of a power property. 1. 32y 322 36yyy 2. 254 255 210444 3. 43x 433 412xxx Exploration: Ex 8: Simplify the expressions by expanding them first using the definition of an exponent . 1. 4xy 444xyxy xy xy xyx x x x y y y yx y 2. 23ab 222 22 23333 339abababa a b ba ba b 3. 42x 444422222216xxxxxxx using the pattern that emerged from the examples above, have students write a rule for raising a product to a power.
8 Power of a Product Property: To find a power of a product, find the power of each factor and multiply. Ex 9: Simplify the expressions using the power of a product property. 1. 4xy 44444xyxyx y 2. 23ab 222222339ababa b 3. 42x 44442216xxx Combining the Properties Ex 10: Simplify the expression 3243x yy . Step One: Power of a product property 333243xyy Step Two: Power of a power property 2 3346342727x y yx y y Step Three: Product of powers property 63 4672727x yx y Algebra I Notes Review Properties of Integer Exponents Integer Exponents Review_Notes Page 4 of 13 5/17/2013 Ex 11: Simplify the expression 223 24a c b c.
9 Step One: Power of a product property 2222324a cbc Step Two: Power of a power property 23 22 22641616a cbca cbc Step Three: Product of powers property 2 1642 1 462 6 5161616a cbca cba b c You Try: Simplify the expression using the Properties of Exponents . 23 55 242rs tr s QOD: Describe the difference between ba and ba , where a and b are whole numbers. Sample Practice Question(s): 1. Evaluate 23x when x = 2. A. 12 B. 16 C. 36 D. 64 2. Determine the value of 233 . A. 9 B. 18 C. 27 D. 81 3. Which expression is equivalent to 353435x y zx y?
10 A. 1295x y z B. 17 125x y z C. 209125x y z D. 17 12125x y z Algebra I Notes Review Properties of Integer Exponents Integer Exponents Review_Notes Page 5 of 13 5/17/2013 Additional Information for Teachers Determine the value of exponential expressions using a variety of methods. Simplify algebraic expressions by applying the Properties of Exponents . Simplify expressions containing negative and zero Exponents . Exploration: Have students use patterns to complete the tables. (Answers are in red.) Note: The pattern is to divide by 2 to move from left to right.
