The document provides examples of exponent laws and polynomial operations. It contains 10 examples of multiplying numbers with exponents, followed by lessons and examples on the laws of exponents including the product law. It then covers lessons and examples of multiplying and dividing polynomials. The goal is for learners to understand exponent laws and be able to perform multiplication and division on polynomials.

2. Find the product.

3. 1. (2)(2)(2)
8

4. 2. (3)(3)(3)
27

5. 3. (5)(5)(5)
125

6. 4. (2)(2)(2)(2)
16

7. 5. (11)(11)
16

8. 6. (1)(1)(1)(1)(1)
1

9. 7. (10)(10)(10
1000

10. 8. (9)(9)(9)
729

11. 9. (3)(3)(3)(3)
81

12. 10. (12)(12)
144

13. Most Essential Learning
Competency:
The learner derives the laws
of exponents and performs
operations on polynomials
(Multiplication and Division).
Code: M7Al-IIe-1, M7Al-IIe-2

14. At the end of the learning period,
you are expected to:
1. derive the laws of exponents
2. perform multiplication and
division on polynomials

15. Lesson:
Laws of Exponents

16. 23 exponent
base

18. (7)(7)(7)(7)(7)(7)(7)(7)
78
Example: Write in exponential form.

19. (y)(y)(y)(y)(y)
y5
Example: Write in exponential form.

20. (ab)(ab)(ab)(ab)
(ab)4
Example: Write in exponential form.

21. Laws of Exponents:
Product Law

22. 33 32
35
Example 1:

23. m3 m4
m7
Example 2:

24. 45 42
47
Example 3:

25. x4 x5
x9
Example 4:

26. n2 n7 n3
n12
Example 5:

28. 24 23
27= 128
Try this!

29. x2 x3 x5
x10
Try this!

30. 2x2 7x3
14x5
Try this!

31. 5m4 3m4
15m8
Try this!

32. 3n2 2n3 5n5
30n10
Try this!

41. =
X-2 = 1
X2
5x = 5. x1-5 = 5x- 4 = 5
x5 1 x4

44. Lesson:
Perform
multiplication and
division
on polynomials

55. Try this!
Perform the
indicated
operation.

56. 1 ( x + 1) (x + 2)
Solution:
x +1
x + 2
= x2 + x +2x +2
x2+3x+2
=
Add the like terms

57. 2 Divide 2x2 +4x+6 by 2x
Solution:
2x2 +4x
2x
= x + 2x
=
= 2x2 + 4x
2x 2x