Queueue 4^-5 + 2^-5 = - Universityku

Queueue
4^-5 + 2^-5 =

Pembuka kata

Hi Sobat Brainly! Pada kali ini, kita akan belajar mengenai eksponen atau perpangkatan.

1). Apa itu perpangkatan?

Perpangkatan ialah suatu operasi hitung bilang bulat yang digunakan untuk menghitung suatu bilangan dengan angka yang sama, sesuai banyak-nya angka yang telah ditentukan. Contohnya : ${7}^{3} = 7 × 7 × 7 = 343$

2). Siapa pencipta perpangkatan?

Perpangkatan itu sendiri diciptakan oleh John Napier, Seorang ilmuwan asal Skotlandia. Joh Napier sendiri juga merupakan penemu logaritma yang kita kenal hingga sekarang.

3). Sifat sifat eksponen

${a}^{m} times {a}^{n} = {a}^{m + n} \ ( {a}^{m} ) {}^{n} = { a}^{m times n} \ (a times b {)}^{n} = {a}^{n} times {b}^{n} \ {a}^{m} div {a}^{n} = {a}^{m - n} \ ( frac{a}{b} {)}^{n} = frac{ {a}^{n} }{ {b}^{n} } \ {a}^{0} = 1 \ {a}^{ - m} = frac{1}{ {a}^{m} }$

4). Contoh soal eksponen

Perpangkatan 2

${1}^{2} = 1 times 1 = 1 \ {2}^{2} = 2 times 2 = 4 \ {3}^{2} = 3 times 3 = 9 \ {4}^{2} = 4 times 4 = 16 \ {5}^{2} = 5 times 5 = 25\ {6}^{2} = 6 times 6 = 36 \ {7}^{2} = 7 times 7 = 49 \ {8}^{2} = 8 times 8 = 64 \ {9}^{2} = 9 times 9 = 81 \ {10}^{2} = 10 times 10 = 100\ {11}^{2} = 11 times 11 = 121 \ {12}^{2} = 12 times 12 = 144 \ {13}^{2} = 13 times 13 = 169 \ {14}^{2} = 14 times 14 = 196 \ {15}^{2} = 15 times 15 times 225$

Perpangkatan 3

${1}^{3} = 1 times 1 times 1 = 1 \ {2}^{3} = 2 times 2 times 2 = 8 \ {3}^{3} = 3 times 3 times 3 = 27\ {4}^{3} = 4 times 4 times 4 = 64 \ {5}^{3} = 5 times 5 times 5 = 125\ {6}^{3} = 6 times 6 times 6 = 256 \ {7}^{3} = 7 times 7 times 7 = 343 \ {8}^{3} = 8 times 8 times 8 = 512 \ {9}^{3} = 9 times 9 times 9 = 729 \ {10}^{3} = 10 times 10 times 10 = 1000\ {11}^{3} = 11 times 11 times 11 = 1331 \ {12}^{3} = 12 times 12 times 12 = 1726 \ {13}^{3} = 13 times 13 times 13 = 2197\ {14}^{3} = 14 times 14 times 14 = 2744\ {15}^{3} = 15 times 15 times 15 = 3375$

Penyelesaian soal

♡ Diketahui

${4}^{ - 5} + {2}^{ - 5} \ \ = frac{1}{ {4}^{5} } + frac{1}{ {2}^{5} }$

♡ Ditanyakan

Hasil akhir eksponen

♡ Dijawabkan

$frac{1}{4 times 4 times 4 times 4 times 4} + frac{1}{2 times 2 times 2 times 2 times 2} \ \ = frac{1}{(16 times 16) times 4} + frac{1}{(8 times 4)} \ \ = frac{1}{256 times 4} + frac{1}{32} \ \ = frac{1}{1.024} + frac{1}{32} \ \ = mathbf{ frac{1}{1.056}}$