Jawaban:

Pendahuluan :

Bilangan berpangkat merupakan bentuk perkalian berulang dari suatu bilangan yang sama.

✿ { Bentuk umum }

a^b = a × a × a × a × a × a = ...

Keterangan :

a = basis

b = pangkat

✿ { Sifat - Sifat Pangkatan }

• a^b × a^c = a^(b+c)

• a^b ÷ a^c = a^(b-c)

• (a^b)^c = a^(b×c)

• a⁰ = 1

• (a^m × a^n )^b = a^mb × a^nb

• a^m × b^m = (a×b)^m

• a^ -m = 1/a^m

✿ { Eksponen menyederhanakan )

= 25³ × 25²

= 25^(³+²)

= 25⁵

= 25 × 25 × 25 × 25 × 25

= 9.765.625

✿ { Pangkatan 1 }

1¹ = 1

2¹ = 2

3¹ = 3

4¹ = 4

5¹ = 5

6¹ = 6

7¹ = 7

8¹ = 8

9¹ = 9

10¹ = 10

11¹ = 11

12¹ = 12

13¹ = 13

14¹ = 14

15¹ = 15

✿ { Pangkat 2 }

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

11² =121

12² = 144

13² = 169

14² = 196

15² = 225

✿ { Pangkat 3 }

1³ = 1

2³ = 8

3³ = 27

4³ =64

5³ = 125

6³ =216

7³ = 343

8³ = 512

9³ = 729

10³ = 1.000

11³ = 1.331

12³ = 1.728

13³ = 2.197

14³ = 2.744

15³ = 3.375

✿ { Pangkat 4 }

1⁴ = 1

2⁴ = 16

3⁴ = 81

4⁴ = 256

5⁴ = 625

6⁴ = 1.296

7⁴ = 2.401

8⁴ = 4.096

9⁴ = 6.561

10⁴ = 10.000

11⁴ = 14.641

12⁴ = 20.736

13⁴ = 28.561

14⁴ = 38.416

15⁴ = 50.625

✿ { Pangkat 5: }

1⁵ = 1

2⁵ = 32

3⁵ = 243

4⁵ = 1.024

5⁵ = 3.125

6⁵ = 7.776

7⁵ = 16.807

8⁵ = 32.768

9⁵ = 59.049

10⁵ = 100.000

11⁵ = 161.051

12⁵ = 248.832

13⁵ = 371.293

14⁵ = 537.824

15⁵ = 759.375

✿ Cara menghitung Bilangan Berpangkat

• Pangakat 1

1¹ = 1

• Pangakat 2

1² = 1 × 1

• Pangkat 3

1³ = 1 × 1 × 1

✿ { Contoh Pangakat 1 }

1¹ = 1 × 1 = 1

2¹ = 2 × 1 = 2

3¹ = 3 × 1 = 3

4¹ = 4 × 1 = 4

5¹ = 5 × 1 = 5

6¹ = 6 × 1 = 6

7¹ = 7 × 1 = 7

8¹ = 8 × 1 = 8

9¹ = 9 × 1 = 9

10¹ = 10 × 1 = 10

11¹ = 11 × 1 = 11

12¹ = 12 × 1 = 12

13¹ = 13 × 1 = 13

14¹ = 14 × 1 = 14

15¹ = 15 × 1 = 15

✿ { Contoh Pangkat 2 }

2² = 2 × 2 = 4

3² = 3 × 3 = 9

4² = 4 × 4 = 16

5² = 5 × 5 = 25

6² = 6 × 6 = 36

7² = 7 × 7 = 49

8² = 8 × 8 = 64

9² = 9 × 9 = 81

10² = 10 × 10 = 100

11² = 11 × 11 = 121

12² = 12 × 12 = 144

13² = 13 × 13 = 168

14² = 14 × 14 = 196

15² = 15 × 15 = 225

16² = 16 × 16 = 256

17² = 17 × 17=289

18² = 18 × 18 = 324

19² = 19 × 19 = 361

20² = 20 × 20 = 400

21² = 21 × 21 = 441

22² = 22 × 22 = 484

23² = 23 × 23 = 529

24² = 24 × 24 = 576

25² = 25 × 25 = 625

26² = 26 × 26 = 676

27² = 27 × 27 = 729

28² = 28 × 28 = 784

29² = 29 × 29 = 841

30² = 30 × 30 = 900

31² = 31 × 31 = 961

33² = 33 × 33 = 1.089

34² = 34 × 34 = 1.156

35² = 35 × 35 = 1.225

36² = 36 × 36 = 1.296

37² = 37 × 37 = 1.369

38² = 38 × 38 = 1.444

39² = 39 × 39 = 1.521

40² = 40 × 40 = 1.600

41² = 41 × 41 = 1.681

42² = 42 × 42 = 1.764

43² = 43 × 43 = 1.849

44² = 44 × 44 = 1.936

45² = 45 × 45 = 2.025

46² = 46 × 46 = 2.116

47² = 47 × 47 = 2.209

48² = 48 × 48 = 2.304

49² = 49 × 49 = 2.401

50² = 50 × 50 = 2.500

✿ { Contoh Pangkat 3 }

2³ = 2 × 2 × 2 = 8

3³ = 3 × 3 × 3 = 27

4³ = 4 × 4 × 4 = 64

5³ = 5 × 5 × 5 = 125

6³ = 6 × 6 × 6 = 216

7³ = 7 × 7 × 7 = 343

8³ = 8 × 8 × 8 = 512

9³ = 9 × 9 × 9 = 729

10³ = 10 × 10 × 10 = 1.000

11³ = 11 × 11 × 11 = 1.331

12³ = 12 × 12 × 12 = 1.728

13³ = 13 × 13 × 13 = 2.197

14³ = 14 × 14 × 14 = 2.744

15³ = 15 × 15 × 15 = 3.375

16³ = 16 × 16 × 16 = 4.096

17³ = 17 × 17 × 17 = 4.913

18³ = 18 × 18 × 18 = 5.832

19³ = 19 × 19 × 19 = 6.859

20³ = 20 × 20 × 20 = 8.000

✿ { Contoh Pangkat 4 }

2⁴ = 2 × 2 × 2 × 2 = 16

3⁴ = 3 × 3 × 3 × 3 = 81

4⁴ = 4 × 4 × 4 × 4 = 256

5⁴ = 5 × 5 × 5 × 5 = 625

6⁴ = 6 × 6 × 6 × 6 = 1.296

7⁴ = 7 × 7 × 7 × 7 = 2.401

8⁴ = 8 × 8 × 8 × 8 = 4.096

9⁴ = 9 × 9 × 9 × 9 = 6.561

10⁴ = 10 × 10 × 10 × 10 = 10.000

11⁴ = 11 × 11 × 11 × 11 = 14.641

12⁴ = 12 × 12 × 12 × 12 = 20.736

13⁴ = 13 × 13 × 13 × 13 = 28.561

14⁴ = 14 × 14 × 14 × 14 = 38.416

15⁴ = 15 × 15 × 15 × 15 = 50.625

✿ { Contoh Pangkat 5 }

2⁵ = 2 × 2 × 2 × 2 × 2 = 32

3⁵ = 3 × 3 × 3 × 3 × 3 = 243

4⁵ = 4 × 4 × 4 × 4 × 4 = 1.024

5⁵ = 5 × 5 × 5 × 5 × 5 = 3.125

6⁵ = 6 × 6 × 6 × 6 × 6 = 7.776

7⁵ = 7 × 7 × 7 × 7 × 7 = 16.807

8⁵ = 8 × 8 × 8 × 8 × 8 = 32.768

9⁵ = 9 × 9 × 9 × 9 × 9 = 59.049

10⁵ = 10 × 10 × 10 × 10 × 10 = 100.000

11⁵ = 11 × 11 × 11 × 11 × 11 = 161.051

12⁵ = 12 × 12 × 12 × 12 × 12 = 248.832

13⁵ = 13 × 13 × 13 × 13 × 13 = 371.293

14⁵ = 14 × 14 × 14 × 14 × 14 = 537.824

15⁵ = 15 × 15 × 15 × 15 × 15 = 759.375

Penyelesaian :

= 2⁴ + 8⁴

= (2 × 2 × 2 × 2) + (8 × 8 × 8 × 8)

= (4 × 2 × 2) + (64 × 8 × 8)

= (8 × 2) + (512 × 8)

= (16) + (4.096)

= 16 + 4.096

= 4.112

= 15 × 16

= 240

Kesimpulan :

2⁴ + 8⁴ = 4.112

15 × 16 = 240

Pelajari lebih lanjut :

" Tentang Bilangan Berpangkat

• yomemimo.com/tugas/47013484

• yomemimo.com/tugas/47010415

" Tentang Perkalian

• yomemimo.com/tugas/47404656

• yomemimo.com/tugas/47435239

Detail jawaban :

❐ Kelas : 9 dan 3

❐ Mapel : Matematika

❐ Materi : Bab 1 - Bilangan Berpangkat

❐ Kode Soal : 2

❐ Kode Kategorisasi : 9.2.1 / 3.2.1

❐ Kata Kunci : Bilangan berpangkat dan Perkalian