1. Rational Exponents & Radicals
Mrs. Daniel- Algebra 1

2. Exponents

3. Definition: Exponent
The exponent of a number says how many times to use that number in a multiplication. It is written as a small number to the right and above the base number.

4. The Zero Exponent Rule
Any number (excluding zero) to the zero power is always equal to one.
Examples:
1000=1
1470=1
550 =1

5. Negative Power Rule

6. Let’s Practice…
5-2
3 4 −1
(-3)-3

7. The One Exponent Rule
Any number (excluding zero) to the first power is always equal to that number.
Examples:
a1 = a
71 = 7
531 = 53

8. The Power Rule (Powers to Powers)
When an exponential expression is raised to a power, multiply the exponents.
Try these…
(w4) (q2)8
3. (x3)4

9. Products to Powers (ab)n = anbn
Distribute the exponent/power to all variables and/or coefficients.
For example:
(6y) 2 = (62)(y2)= 36y2
(7x3)2 = (7)2(x3)2 = 49x6

10. Let’s Practice… (5x2)2 4. (6x4)2 2. (3wk3)3 5. (n5)2(4mn-2)3
3. (-2y) (5x2)-2

11. The Quotient Rule

12. Let’s Practice…

13. Power of a Fraction

14. Let’s Practice… −2

16. Simplifying Radicals

17. Radical Vocab

18. How to Simplify Radicals
Make a factor tree of the radicand.
Circle all final factor pairs.
All circled pairs move outside the radical and become single value.
Multiply all values outside radical.
Multiply all final factors that were not circled. Place product under radical sign.

20. Let’s Practice…

21. Let’s Practice…

22. How to Simplify Cubed Radicals
Make a factor tree of the radicand.
Circle all final factor groups of three.
All circled groups of three move outside the radical and become single value.
Multiply all values outside radical.
Multiply all final factors that were not circled. Place product under radical sign.

23. Let’s Practice…

24. Simplifying Rational Exponents

25. Review: Radical Vocab

26. Code: Fractional Exponents

27. Let’s Practice #1
Rewrite each of the following as a single power of 7:

28. Let’s Practice #2
Rewrite each of the following in radical form: − 1 4

29. Let’s Practice #3 Simplify, if possible: 8 1 3 16 1 2 + 27 1 3
8 1 3

30. Let’s Practice #4 Which is equivalent to a 1 2 ∙ b 3 4 ? a b 3

31. Let’s Practice #5
Which is equivalent to 3 a 2 ?
a 3 2
a 2 3
a 1 6
a 6

32. Let’s Practice #6
Simplify. Rewrite each of the following as a single power of ( )( 7 − 1 4 ) Rewrite 8 ⋅ as a single power of 2.

33. Let’s Practice #7
Rewrite as radical expressions, then simplify, if possible:
12 𝑎 2 3
6 𝑥 5 2
64 𝑎 4 5

34. Mini Quiz
Is each statement, true or false. Explain!!!!

35. Applications

36. Applications

37. Applications
The volume of a cube is related to the area of a face by the formula V = 𝐴 What is the volume of a cube whose face has an area of 100 cm2

38. Rational & Irrational Numbers

39. Rational Numbers
Any number that can be expressed as the quotient or fraction 𝑝 𝑞 of two integers.
YES:
Any integers
Any decimals that
ends or repeats
Any fraction
NO:
Never ending decimals

40. Irrational Numbers Any number that can not be expressed as a fraction.
Usually a never-ending, non-repeating decimal.
Examples: 𝜋
2 , 5 ….

41. Let’s Practice…
Rational or Irrational.
2 17
1 3

42. Will it be Rational or Irrational?
Sums: Rational + Rational = Rational + Irrational = Irrational + Irrational = Products: Rational x Rational = Rational x Irrational = Irrational x Irrational =

43. Rational or Irrational?
Is the sum of and rational or irrational?
Is the sum of 4.2 and rational or irrational?
Determine if the product of and is rational or irrational.

46. Advanced Rational Expressions