7.3 RATIONAL EXPONENTS NOTES
(DAY 1)
Rational exponents are…exponents that contain ____________. We can also rewrite them using ___________!
Evaluate the following using a calculator…what do you notice?
1
1
A. 252 =
C. 1002 =
B. √25=
D. √100=
SQUARE ROOT
DEFINITION:
PRACTICE! 
1
A. 492 =
B. √12 =
D. 2√𝑎=
E. 92 =
1
C. 𝑏 2 =
1
WHAT IF…
F. √3𝑥 =
EXAMPLE #1
2
√16 𝑜𝑟
1
162
Break Down: ____ ● ____
Answer:
EXAMPLE #2
1
812
√100 𝑜𝑟 _____
Break Down: ____ ● ____
Answer:
Break Down: ____ ● ____
Answer:
This is asking us to split up each base number into two equal pieces, and then take _____ out of the two factors as our answer!
________________________________________________________________________________________
We can also use the same logic for something like…
WHAT IF….
EXAMPLE #1
1
814
Break Down: __ ● __ ●__ ● __
Answer:
EXAMPLE #2
1
273
5
√32 𝑜𝑟 _____
Break Down: ___ ● ___ ● ___
Answer:
EXAMPLE #3
Break Down: __●__●__●__●__
Answer:
EXAMPLE #4
th
N ROOT DEFINITION:
1
643
3
√125
Last time…I swear!  Use the same logic to explore the last definition.
WHAT IF…
EXAMPLE #1
EXAMPLE #2
3
164
2
273
2
Break Down: __ ● __ ●__ ● __
Answer:
Break Down: ____ ● ____● ____
Answer:
EXAMPLE #3
EXAMPLE #4
2
643
5
3
( √36) 𝑜𝑟 ______
2
( √32) 𝑜𝑟 ______
Use this space for any extra notes you may want to take! 
Break Down: ____ ● ____
Answer:
ADVANCED ROOT
DEFINITION:
Section 7.3 – Homework Worksheet Day 1
PART 1: SQUARE ROOT DEFINITION
1
2. Find 492
1. Find √121
1
3. Rewrite (3𝑥)2 into radical form
4. Rewrite √33𝑦 into exponential form
PART 2: Nth ROOT DEFINITION
1
1
5. Find 646
6. Find 2564
1
7. Rewrite 3008 into radical form
8. Rewrite 6√2𝑦 into exponential form
PART 3: ADVANCED Nth ROOTS
5
2
9. Find 164
10. What is 2163 ?
2
11. Rewrite 455 into radical form
7
12. Rewrite √(5𝑥)4 into exponential form