©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