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Urutan bilangan 2−35, 3−25, dan 5−15 dari yang terkecil ke yang terbesar adalah ....

Pertanyaan

Urutan bilangan 2 to the power of negative 35 end exponent comma space 3 to the power of negative 25 end exponent comma space text dan end text space 5 to the power of negative 15 end exponent dari yang terkecil ke yang terbesar adalah ....

  1. 2 to the power of negative 35 end exponent comma space 3 to the power of negative 25 end exponent comma space text dan end text space 5 to the power of negative 15 end exponent

  2. 3 to the power of negative 25 end exponent comma space 2 to the power of negative 35 end exponent comma space text dan end text space 5 to the power of negative 15 end exponent

  3. 3 to the power of negative 25 end exponent comma space 5 to the power of negative 15 end exponent comma space text dan end text space 2 to the power of negative 35 end exponent

  4. 5 to the power of negative 15 end exponent comma space 3 to the power of negative 25 end exponent comma space text dan end text space 2 to the power of negative 35 end exponent

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Berdasarkan sifat bilangan berpangkat yaitu a to the power of negative n end exponent equals 1 over a to the power of n comma space a not equal to 0 maka bilangan 2 to the power of negative 35 end exponent comma space 3 to the power of negative 25 end exponent comma space text dan end text space 5 to the power of negative 15 end exponent ekuivalen dengan

2 to the power of negative 35 end exponent equals 1 over 2 to the power of 35 3 to the power of negative 25 end exponent equals 1 over 3 to the power of 25 5 to the power of negative 15 end exponent equals 1 over 5 to the power of 15

Berdasarkan sifat bilangan berpangkat yaitu 1 to the power of m equals 1 dan open parentheses a over b close parentheses to the power of m equals a to the power of m over b to the power of m comma b not equal to 0 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 to the power of negative 35 end exponent end cell equals cell 1 over 2 to the power of 35 end cell row blank equals cell 1 to the power of 35 over 2 to the power of 35 end cell row blank equals cell open parentheses 1 half close parentheses to the power of 35 end cell row cell 3 to the power of negative 25 end exponent end cell equals cell 1 over 3 to the power of 25 end cell row blank equals cell 1 to the power of 25 over 3 to the power of 25 end cell row blank equals cell open parentheses 1 third close parentheses to the power of 25 end cell row cell 5 to the power of negative 15 end exponent end cell equals cell 1 over 5 to the power of 15 end cell row blank equals cell 1 to the power of 15 over 5 to the power of 15 end cell row blank equals cell open parentheses 1 fifth close parentheses to the power of 15 end cell end table

Berdasarkan sifat bilangan berpangkat yaitu open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent maka

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 to the power of negative 35 end exponent end cell equals cell open parentheses 1 half close parentheses to the power of 35 end cell row blank equals cell open parentheses 1 half close parentheses to the power of 7 cross times 5 end exponent end cell row blank equals cell open parentheses open parentheses 1 half close parentheses to the power of 7 close parentheses to the power of 5 end cell row blank equals cell open parentheses 1 to the power of 7 over 2 to the power of 7 close parentheses to the power of 5 end cell row blank equals cell open parentheses 1 over 128 close parentheses to the power of 5 end cell end table

Sedangkan table attributes columnalign right center left columnspacing 0px end attributes row cell 3 to the power of negative 25 end exponent end cell equals cell open parentheses 1 third close parentheses to the power of 25 end cell end table diperoleh sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 to the power of negative 25 end exponent end cell equals cell open parentheses 1 third close parentheses to the power of 25 end cell row blank equals cell open parentheses 1 third close parentheses to the power of 5 cross times 5 end exponent end cell row blank equals cell open parentheses open parentheses 1 third close parentheses to the power of 5 close parentheses to the power of 5 end cell row blank equals cell open parentheses 1 to the power of 5 over 3 to the power of 5 close parentheses to the power of 5 end cell row blank equals cell open parentheses 1 over 243 close parentheses to the power of 5 end cell end table

Sedangkan table attributes columnalign right center left columnspacing 0px end attributes row cell 5 to the power of negative 15 end exponent end cell equals cell open parentheses 1 fifth close parentheses to the power of 15 end cell end table diperoleh sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 to the power of negative 15 end exponent end cell equals cell open parentheses 1 fifth close parentheses to the power of 15 end cell row blank equals cell open parentheses 1 fifth close parentheses to the power of 3 cross times 5 end exponent end cell row blank equals cell open parentheses open parentheses 1 fifth close parentheses cubed close parentheses to the power of 5 end cell row blank equals cell open parentheses 1 cubed over 5 cubed close parentheses to the power of 5 end cell row blank equals cell open parentheses 1 over 125 close parentheses to the power of 5 end cell end table

Jika terdapat pecahan-pecahan dengan nilai pembilang sama maka cara untuk mengurutkan pecahan adalah dengan melihat nilai penyebutnya yaitu pecahan dengan nilai penyebut besar memiliki nilai yang lebih kecil sehingga

1 over 243 less than 1 over 128 less than 1 over 125 open parentheses 1 over 243 close parentheses to the power of 5 less than open parentheses 1 over 128 close parentheses to the power of 5 less than open parentheses 1 over 125 close parentheses to the power of 5

Jadi Urutan bilangan 2 to the power of negative 35 end exponent comma space 3 to the power of negative 25 end exponent comma space text dan end text space 5 to the power of negative 15 end exponent dari yang terkecil ke yang terbesar adalah  3 to the power of negative 25 end exponent comma space 2 to the power of negative 35 end exponent comma space text dan end text space 5 to the power of negative 15 end exponent.

Oleh karena itu, jawaban yang benar adalah B.

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