©Sarah’s School of Math 2015

Exponential Unit Lesson 2 Name: ___________________

Rational Exponent Rules Guided Notes Part 1: Investigation of Rational Exponents:

1. √823 = 823 =

2. √2743 = 2743 =

3. √163 = 1632 =

4. √645 = 6452 =

5. √1253 = 12513 =

6. √100 = 10012 =

7. √643 = 6413 =

8. √49 = 4912 =

9. √164 = 1614 =

Part 2: Rewrite using rational exponents:

1. √64𝑥3𝑦2𝑧63 = 2. √81𝑥5𝑦12𝑧44 =

3. √49𝑥6𝑦2𝑧7 = 4. √32𝑥5𝑦3𝑧25 =

Part 3: Simplify using all the rules of exponents (multiple choice):

1. (𝑥13)−6

𝑎. √𝑥 𝑏. 𝑥2 𝑐.1

𝑥18 𝑑.1

𝑥2

2. (𝑦12)−8

𝑎. √𝑦 𝑏. 𝑦4 𝑐.1

𝑦4 𝑑.1

𝑦16

what pattern do you notice?

©Sarah’s School of Math 2015

3. (𝑧−14)12

𝑎.1𝑧3 𝑏. 𝑧3 𝑐. √𝑧 𝑑.

1𝑧48

4. (𝑥14)2

𝑎.1

𝑥8 𝑏. 𝑥2 𝑐. √𝑥 𝑑.1

𝑥2

5. (19)−1

2

𝑎. −4.5 𝑏. 3 𝑐. −3 𝑑.13

6. ( 164

)−13

𝑎. 4 𝑏. −4 𝑐.643 𝑑.

14

7. (49)−12

𝑎. −24.5 𝑏. 7 𝑐. −7 𝑑.17

8. ( 181

)12

𝑎. −40.5 𝑏. −9 𝑐.19 𝑑. 9

Part 4: All the rules together! Simplify:

1. (−7𝑎5)4 2. 𝑎4𝑏8

𝑎𝑏2 3. 𝑅𝑒𝑤𝑟𝑖𝑡𝑒 𝑢𝑠𝑖𝑛𝑔 𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡𝑠: √27𝑎3𝑏73

4. (3𝑥2)0 5.(12)−3 6. (−2𝑥3𝑦4)(−9𝑥3𝑦𝑧8) 7. (𝑥−3

2)2 Part 5: On your own!!!

1. 𝑅𝑒𝑤𝑟𝑖𝑡𝑒 𝑢𝑠𝑖𝑛𝑔 𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡𝑠: √8𝑎2𝑏3𝑐93

2. 𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦: (𝑥15)−5 3. 𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦: ( 1

36)−1

2