[tex]1). \: {21}^{2} \times {25}^{2} \\ 2). \: {14}^{2} - {13}^{2} [/tex]
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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
✿ Perkalian adalah operasi matematika penskalaan satu bilangan dengan bilangan lain perkalian disimbolkan dengan tanda kali (×).
Sifat - sifat Perkalian :
( - ) × ( - ) = ( + )
( - ) × ( + ) = ( - )
( + ) × ( - ) = ( - )
Contoh perkalian 1 :
1 × 1 = 1
2 × 1 = 2
3 × 1 = 3
4 × 1 = 4
5 × 1 = 5
6 × 1 = 6
7 × 1 = 7
8 × 1 = 8
9 × 1 = 9
10 × 1 = 10
Contoh perkalian 2 :
1 × 2 = 2
2 × 2 = 4
3 × 2 = 6
4 × 2 = 8
5 × 2 = 10
6 × 2 = 12
7 × 2 = 14
8 × 2 = 16
9 × 2 = 18
10 × 2 = 20
Contoh perkalian 3 :
1 × 3 = 3
2 × 3 = 6
3 × 3 = 9
4 × 3 = 12
5 × 3 = 15
6 × 3 = 18
7 × 3 = 21
8 × 3 = 24
9 × 3 = 27
10 × 3 = 30
Penyelesaian :
= 21² × 25²
= (21 × 21) × (25 × 25)
= 441 × 625
= 275.625
= 14² - 13²
= (14 × 14) - (13 × 13)
= 196 - 169
= 27
Kesimpulan :
21² × 25² = 275.625
14² - 13² = 27
Pelajari lebih lanjut :
" Tentang Bilangan Berpangkat
• https://brainly.co.id/tugas/47014842
• https://brainly.co.id/tugas/47013484
• https://brainly.co.id/tugas/47010415
Detail jawaban :
❐ Kelas : 9
❐ Mapel : Matematika
❐ Materi : Bab 1 - Bilangan Berpangkat
❐ Kode Soal : 2
❐ Kode Kategorisasi : 9.2.1
❐ Kata Kunci : Bilangan berpangkat
Jawaban:
[tex] \sf {21}^{2} \times {25}^{2} [/tex]
[tex] \sf(21 \times 21) \times (25 \times 25)[/tex]
[tex] \sf441 \times 625[/tex]
[tex] \sf = 275.625[/tex]
_______
[tex] \sf {14}^{2} - {13}^{2} [/tex]
[tex] \sf(14 \times 14) - (13 \times 13)[/tex]
[tex] \sf196 - 169[/tex]
[tex] \sf = 27[/tex]
