1. S.K.1. Memecahkan masalah yang
berkaitan dengan Konsep
Operasi Bilangan Real
K.D.2. Menerapkan Operasi pada
Bilangan Berpangkat
( Exponent )
Tujuan Pembelajaran :
Siswa dapat mengoperasikan
bilangan berpangkat
2. Siswa dapat menyederhanakan

2. EXPONENT Rene Descartes(1550-1617)
A France mathematician, introduced the method of writing exponent for the first time

3. MAIN TOPIC
Definition of The Positive Integer Exponent
In junior high school, you had learned about exponential number with base 10. the positive integer exponent implies how many copies of the base are multiplied together
(Bilangan Berpangkat adalah suatu cara perkalian dengan bilangan yang sama)
Example:
an = a x a x a x … x a , sebanyak n faktor
34 = 3 x 3 x 3 x 3
57 = 5 x 5 x 5 x 5 x 5 x 5 x 5

4. ba = c if b Definition of Exponent
b = cardinal number ( bilangan pokok )
a = exponent number ( bilangan pangkat )
c = exponent of the number ( bilangan hasil perpangkatan )
Example : = 9
if , then = a 2 2

5. The Properties of Exponent ( Formula )1 2 3 4 5

6. The Properties of Exponent6 7 8 9

7. Example aplication formula
aⁿ = a . a . a ….. a , sebanyak n faktor
Contoh :
a³ = a . a . a
2³ =
aᵐ . aⁿ = aᵐ ⁺ ⁿ
a³ . a⁴ = a³ ⁺ ⁴ = a⁷
a⁶ . aˡ . a⁵ = a ⁶ ⁺ ˡ ⁺ ⁵ = aᴵ² , (a sebagai bilangan
pokok harus sama)

8. 3. aᵐ : aⁿ = aᵐ ̄ ⁿ Contoh : a⁸ : a² = a ⁸ ̄ ² = a⁶ a³. b⁴ = a³. a ̄ ⁵
3. aᵐ : aⁿ = aᵐ ̄ ⁿ Contoh : a⁸ : a² = a ⁸ ̄ ² = a⁶ a³ . b⁴ = a³ . a ̄ ⁵ . b ⁴ . b ̄ ⁷ = a³ ̄ ⁵ . b ⁴ ̄ ⁷ a⁵ . b⁷ = a ̄ ² . b ̄ ³ 4. ( aᵐ )ⁿ = aᵐ·n ( a³ )² = a³·² = a⁶ {(a³)²}⁴ = a³·²·⁴ = a²⁴ ( a³ . b )⁴ = a³·⁴ . b ⁴ = aˡ² . b⁴ a ² ⁵ = aˡ⁰ b ³ bˡ⁵

9. ᵐ√aⁿ = a n/m
Contoh :
⁵√a³ = a3/5
√a = ²√aˡ = a1/2
√x = x1/2
x² . √x = x² . X 1/2 = x²⁺1/2 = x5/2 = x² 1/2
a ̄ ⁿ = 1/aⁿ , aⁿ = 1/a ̄ ⁿ
3 ̄ ² = 1/3² = 1/ , 3² = 1/3 ̄ ²
2 ̄ ³ = 1/2³ = 1/ , 2³ = 1/2 ̄ ³
a⁰ = 1
10000 ⁰ = 1

10. Example 1:
Simplify the following expressions!
a. ((6a2b3)2)4
b. (23a2b3)4 x (2ab2)3
Answer :
a. ((6a2b3)2) = (62.a2x2.b3x2)4
= (62.a4.b6)4
= 68.a16.b24

11. b. (23a2b3)4 x (2ab2)3
Answer :
= (23a2b3)4 x (2ab2)3
= (23x4 . a2x4 . b3x4) x (23 . a3 . b2x3)
= (212 . a8. b12) x (23 . a3 . b6)
= ( a8+3 . b12+6)
= 215. a11 . b18

12. Example 2: a. 2p3q-4 b. a-7b5c-9 : 10-10c7d-6 c. (5-2m2n-5)-4
Simplify and state each of the following expressions in their positive integer exponents!
a. 2p3q-4
b. a-7b5c-9 : 10-10c7d-6
c. (5-2m2n-5)-4

13. Answer : 1. 2p3q-4 = 2. a-7b5c-9 : 10-10c7d-6 = =
3. (5-2m2n-5) = m n-5.-4
= 58 m-8 n20

14. Competence Check: Simplify the following expressions! a. ((-6a2b3)2)4
b. (23a2b3)4 x (2ab2)3 c.
Simplify and state each of the following expressions in their positive integer exponents! a. b.
c. (5a2b-3)-3 . 3(a2b3)2

15. ROOT
There are so many phenomena in our life which Can be modeled to the function or equation containing roots.
Let start our discussion about concept of roots by studying the rational and irrational number first

16. Definition of Rational and Irrational Numbers
Rational numbers are numbers that can be expressed as fraction a/b, where a and b are integers and b 0

17. Definition of Root
Root are numbers in the root symbol which cannot produce rational numbers
Example : ,
03:13:58

18. Addition and Subtraction of the roots
Algebra Operation Of The Roots
Addition and Subtraction of the roots
b. Multiplication of Roots
There are several properties of multiplication of roots, such as: 1. 2. 3.

19. Example: Study the following addition and subtraction a. b.
Simplify there following expression

20. Answer : a. b. =

21. Simplifying the Form of :

22. Example :
Simplify each of the following roots!
Answer :
a b.

23. Rationalizing the Denominator of Fraction:

24. Thank You