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**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

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**EXPONENT Rene Descartes(1550-1617)**

A France mathematician, introduced the method of writing exponent for the first time

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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

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**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

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**The Properties of Exponent ( Formula )**

1 2 3 4 5

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**The Properties of Exponent**

6 7 8 9

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**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)

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**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

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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

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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

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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

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**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

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**Answer : 1. 2p3q-4 = 2. a-7b5c-9 : 10-10c7d-6 = =**

3. (5-2m2n-5) = m n-5.-4 = 58 m-8 n20

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**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

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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

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**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

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

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**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.

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**Example: Study the following addition and subtraction a. b.**

Simplify there following expression

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Answer : a. b. =

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**Simplifying the Form of :**

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

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**Rationalizing the Denominator of Fraction:**

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Thank You

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Ch. 7.4 Rational Exponents p. 379. Rational Exponents If the nth root of a is a real number and m is an integer, then: and If m is negative, a ≠ 0.

Ch. 7.4 Rational Exponents p. 379. Rational Exponents If the nth root of a is a real number and m is an integer, then: and If m is negative, a ≠ 0.

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