Priskeylaseptiani8idn
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Dengan menggunakan sifat [tex]$(a \times b)^n = a^n \times b^n$[/tex]:

a. [tex]$\left(3^2 a^5\right)^2$[/tex]

b. [tex]$\left(a^2 b^3 c\right)^5$[/tex]

Sagot :

GinnyAnsweridn
Tentu, mari kita selesaikan soal ini dengan menggunakan sifat eksponen [tex]\((a \times b)^n = a^n \times b^n\)[/tex].

### Bagian (a): [tex]\(\left(3^2 a^5\right)^2\)[/tex]

1. Tulis ulang ekspresi:
[tex]\[ \left(3^2 \times a^5\right)^2 \][/tex]

2. Terapkan sifat eksponen [tex]\((a \times b)^n = a^n \times b^n\)[/tex]:
[tex]\[ (3^2)^2 \times (a^5)^2 \][/tex]

3. Hitung masing-masing eksponen:
[tex]\[ (3^2)^2 = 3^{2 \times 2} = 3^4 \][/tex]
[tex]\[ (a^5)^2 = a^{5 \times 2} = a^{10} \][/tex]

4. Gabungkan hasilnya:
[tex]\[ 3^4 \times a^{10} \][/tex]

5. Hitung [tex]\(3^4\)[/tex]:
[tex]\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \][/tex]

6. Jadi hasil akhir untuk bagian (a) adalah:
[tex]\[ 81 \times a^{10} \][/tex]

### Bagian (b): [tex]\(\left(a^2 b^3 c\right)^5\)[/tex]

1. Tulis ulang ekspresi:
[tex]\[ \left(a^2 \times b^3 \times c\right)^5 \][/tex]

2. Terapkan sifat eksponen [tex]\((a \times b \times c)^n = a^n \times b^n \times c^n\)[/tex]:
[tex]\[ (a^2)^5 \times (b^3)^5 \times c^5 \][/tex]

3. Hitung masing-masing eksponen:
[tex]\[ (a^2)^5 = a^{2 \times 5} = a^{10} \][/tex]
[tex]\[ (b^3)^5 = b^{3 \times 5} = b^{15} \][/tex]
[tex]\[ c^5 \][/tex]

4. Gabungkan hasilnya:
[tex]\[ a^{10} \times b^{15} \times c^5 \][/tex]

Jadi hasil akhir untuk bagian (b) adalah:

[tex]\[ a^{10} \times b^{15} \times c^5 \][/tex]
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