1. Unit 1 Day 4 Radical & Rational Exp. Practice
Objectives: Simplify a rational exponent and radical expression by changing the base or factoring. Rewrite and evaluate a radical with rational exponents, and a number with a rational exponent in radical notation. Use properties of rational exponents to evaluate and simplify expressions.
Standards: Apply and extend the properties of exponents to solve problems with rational exponents.
Supplementary Reading: ???

2. Warmup
Convert the following from radical to rational exponent notation or vice versa. Then Simplify
3 16𝑥 𝑥 − 1 2

3. Applying What We Know
Use the properties of exponents to rewrite the following
See how the following are unable to be combined due to different bases…D-D-DROP THE BASE
2 2 =4 →
3 2 =9 →
4 5
9 3
4 5
9 3 =
1024
729 =
( 2 2 ) 5
( 3 2 ) 3 =
2 10
3 6
2 10
3 6
∗ ∗𝑥
3∗ −4∗ 𝑥

4. Applying What We Know Expand the following 𝑥+2 2 𝑥 2 + 2 2 ≠
Does it Make sense that that would work with fractional exponents?...
Look for another Method…
𝑥+2 2
𝑥+2 3 ≠ 𝑥 𝑥
𝑥 2 +4𝑥+4 1/2
3 𝑥 3 +4 𝑥 2 +2𝑥+8

5. Check For Understanding
2𝑥− 3 𝑥 3 𝑥 −5
3 𝑥 2 8
( 4𝑥 2 −12𝑥+9)
3 ( 𝑥 3 −27)

6. Annoying Game!!!
Get a sheet notebook paper out. Only calculators & Pencils. NO NOTES!!!
Rules = answer the question on the board.
Get called on.
Claim your prize.

7. Vocab & Concepts Practice
N nth root is simplified if the following 3 conditions are all true:
1.)
2.)
3.)

8. Vocab & Concepts Practice
In , the 3 is called the _________

9. Vocab & Concepts Practice
In , the 47 is called the _________

10. Vocab & Concepts Practice
The process of moving removing the radical from the denominator is called ________________

11. Vocab & Concepts Practice
What is the conjugate of 2- 𝑥 ?

12. Vocab & Concepts Practice
What is the conjugate of 𝑥 +2?

13. Vocab & Concepts Practice
What is the conjugate of 7−3 2𝑥 ?

14. Vocab & Concepts Practice
What is the conjugate of 𝑥 − 3𝑥 ?

15. Practice
Simplify Using Properties of Exponents

16. Practice
Simplify Using Properties of Exponents

17. Practice
Simplify Using Properties of Exponents

18. Practice
Simplify Using Properties of Exponents

19. Practice
Simplify Using Properties of Exponents

20. Practice
Simplify Using Properties of Exponents

21. Practice
Simplify Using Properties of Exponents

22. Practice
Simplify Using Properties of Exponents

23. Closure
Simplify the following
𝑥−2 ( 𝑥 2 −4𝑥+4)