SOAL LATIHAN

1. Dengan menggunakan sifat bilangan, sederhanakan bentuk-bentuk berikut:

a) 26 x 2

9

b) a10

x a-9

c) (66)

5

d) 5-2

: 57

e) a8 : b

-3

f) (a3 x a

5)

6

2. Dengan menggunakan sifat bilangan, sedehanakan bentuk-bentuk berikut:

a) 26/5 x 21/3

b) 𝑎7/2 x 𝑎8/5

c) 32/5 x 36/6

d) 𝑏5/3 : 𝑏−7/4

e) (𝑎5/3 x 𝑎3/5)3

3. Sederhanakan bentuk-bentuk berikut:

a) 34 + 32 - 37

b) 26 - 28 + 183

c) 55 + 204 - 452

d) 67 - 243 - 966

4. Sederhanakan perkalian-perkalian berikut ini

a) 73 x 84

b) 85 x 36

c) 3 53 x 2 74

d) 6√435 x 5√623

5. Rasionalkan pecahan berikut:

a) 2

√8

b) 3

8+ √5

c) 4

√7− √10

d) 12

√7− √6

6. Sederhanakanlah bentuk pangkat berikut:

a) (x + y)5

b) (x – y)4

c) (2x + 3y)5

d) (3x-2y)4

JAWABAN

1. a) 26 x 2

9 = 2

6+9 = 2

15

b) a10

x a-9

= a10+(-9)

= a1

c) (66)

5 = 6

6x5 = 6

30

d) 5-2

: 57 = 5

(-2)-7 = 5

-9

e) a8 : b

-3 =

f) (a3 x a

5)

6 = a

3x6 x a

5x6 = a

18 x a

30 = a

18+30 = a

48

2. a) 26/5 𝑥 21/3 = 2(18+5)

15)

= 223/15

b) 𝑎7/2 𝑥 𝑎8/5 = 𝑎(

35+16

10)

= 𝑎51/10

c) 32/5𝑥 36/6 = 3(2

5−

1

1)

= 3(2−5

5)

= 3−3/5

d) 𝑏5/3 𝑥 𝑏−7/4 = 𝑏(20+21

12)

= 𝑏41/12

e) (𝑎5/3 𝑥 𝑎3/5)3 = (𝑎34/15))3

= 𝑎34/5

3. a) 34 + 32 - 37 = - 3

b) 26 - 28 + 183 = 22 + 29

= 27

c) 55 + 204 - 452 = 55 + 5.44 - 5.92

= 55 + 52.4 - 53.2

= 55 + 58 - 56

= 57

d) 67 - 243 - 966 = 67 + 6.43 - 6.166

= 67 + 62.3 - 64.6

= 67 + 66 - 624

= 623

4. a) 73 x 84 = 8.74.3

= 5612

b) 85 x 36 = 3.86.5

= 2430

c) 3 53 x 2 74 = 527 x 716

= 7.516.27

= 35432

d) 6√435 x 5√623

= 64774.7 x 36125

= 304.2000.972

5. a) 2

√8 =

2

√8 x

√8

√8 =

2√8

8

b) 3

8+ √5 =

3

8+ √5 x

8− √5

8− √5

= 3(8− √5)

64−5

= 24−3√5

59

c) 4

√7− √10 =

4

√7− √10 x

√7+ √10

√7+ √10

= 4(√7+ √10)

7−10

= 4(√7+ √10)

−3

d) 12

√7+ √6 =

12

√7− √6 x

√7+ √6

√7+ √6

= 12(√7− √6)

7−6

= 12(√7− √6)

1

= 12(√7 − √6)

6. a) (x + y)5 = x

5 + 5x

4y + 10x

3y

2 +10x

2y

3 + 5xy

4 + y

5

b) (x – y)4 = x

4 – 4x

3y + 6x

2y

2 – 6x

2y

3 + y

4

c) (2x + 3y)5 =

(2x)

5 + 5(2x)

4(3y) + 10(2x)

3(3y)

2 + 10(2x)

2(3y)

3 + 5(2x)(3y)

4 + (3y)

5

= 32x5 + 5.16x

4.3y + 10.8x

3.9y

2 + 10.4x

2.27y

3 + 5.2x.81y

4 + 243y

5

= 32x5 + 240x

4y + 720x

3y

2 + 1.080x

2y

3 + 810xy

4 + 243y

5

d) (3x-2y)4 = (3x)

4 – 4(3x)

3(2y) + 6(3x)

2(2y)

2 – 4(3x)(2y)

3 + (2y)

4

= 81x4 – 4.27x

3.2y + 6.9x

2.4y

2 – 4.3x.8y

3 + 16y

4

= 81x4 – 216x

32y + 216x

2y

2 – 96xy

3 + 16y

4