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Bentuk sederhana dari (2−43−2522−33−25−2​)2 adalah ....

Pertanyaan

Bentuk sederhana dari begin mathsize 14px style open parentheses fraction numerator 2 to the power of negative 3 end exponent space 3 to the power of negative 2 end exponent space 5 to the power of negative 2 end exponent over denominator 2 to the power of negative 4 end exponent space 3 to the power of negative 2 end exponent space 5 squared end fraction close parentheses squared end style adalah ....

  1. begin mathsize 14px style 2 to the power of 4 over 5 to the power of 8 end style 

  2. begin mathsize 14px style 2 squared over 5 to the power of 8 end style 

  3. begin mathsize 14px style 3 squared over 2 to the power of 8 end style 

  4. begin mathsize 14px style fraction numerator 2 to the power of 4 over denominator 3 squared space 5 squared end fraction end style 

  5. begin mathsize 14px style fraction numerator 2 to the power of 4 over denominator 5 to the power of 1 space 3 squared end fraction end style 

Pembahasan:

Berdasarkan sifat bilangan berpangkat yaitu a to the power of m divided by a to the power of n equals a to the power of m minus n end exponent dan a to the power of 0 equals 1 comma a not equal to 0 maka begin mathsize 14px style open parentheses fraction numerator 2 to the power of negative 3 end exponent space 3 to the power of negative 2 end exponent space 5 to the power of negative 2 end exponent over denominator 2 to the power of negative 4 end exponent space 3 to the power of negative 2 end exponent space 5 squared end fraction close parentheses squared end style diperoleh sebagai berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 2 to the power of negative 3 end exponent space 3 to the power of negative 2 end exponent space 5 to the power of negative 2 end exponent over denominator 2 to the power of negative 4 end exponent space 3 to the power of negative 2 end exponent space 5 squared end fraction close parentheses squared end cell equals cell open parentheses 2 to the power of negative 3 minus open parentheses negative 4 close parentheses end exponent times 3 to the power of negative 2 minus open parentheses negative 2 close parentheses end exponent times 5 to the power of negative 2 minus 2 end exponent close parentheses squared end cell row blank equals cell open parentheses 2 to the power of negative 3 plus 4 end exponent times 3 to the power of negative 2 plus 2 end exponent times 5 to the power of negative 4 end exponent close parentheses squared end cell row blank equals cell open parentheses 2 to the power of 1 times 3 to the power of 0 times 5 to the power of negative 4 end exponent close parentheses squared end cell row blank equals cell open parentheses 2 times 1 times 5 to the power of negative 4 end exponent close parentheses squared end cell row blank equals cell open parentheses 2 times 5 to the power of negative 4 end exponent close parentheses squared end cell end table

Berdasarkan sifat bilangan berpangkat open parentheses a cross times b close parentheses to the power of m equals a to the power of m cross times b to the power of mopen 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 dan a to the power of negative n end exponent equals 1 over a to the power of n maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 2 to the power of negative 3 end exponent space 3 to the power of negative 2 end exponent space 5 to the power of negative 2 end exponent over denominator 2 to the power of negative 4 end exponent space 3 to the power of negative 2 end exponent space 5 squared end fraction close parentheses squared end cell equals cell open parentheses 2 to the power of negative 3 minus open parentheses negative 4 close parentheses end exponent space 3 to the power of negative 2 minus open parentheses negative 2 close parentheses end exponent space 5 to the power of negative 2 minus 2 end exponent close parentheses squared end cell row blank equals cell open parentheses 2 cross times space 5 to the power of negative 4 end exponent close parentheses squared end cell row blank equals cell 2 squared cross times open parentheses 5 to the power of negative 4 end exponent close parentheses squared end cell row blank equals cell 2 squared cross times 5 to the power of negative 8 end exponent end cell row blank equals cell 2 squared cross times 1 over 5 to the power of 8 end cell row blank equals cell 2 squared over 5 to the power of 8 end cell end table 

Jadi, bentuk sederhana dari begin mathsize 14px style open parentheses fraction numerator 2 to the power of negative 3 end exponent space 3 to the power of negative 2 end exponent space 5 to the power of negative 2 end exponent over denominator 2 to the power of negative 4 end exponent space 3 to the power of negative 2 end exponent space 5 squared end fraction close parentheses squared end style adalah begin mathsize 14px style 2 squared over 5 to the power of 8 end style.

Oleh karena itu, jawaban yang tepat adalah B.

Jawaban terverifikasi

Dijawab oleh:

R. Febrianti

Mahasiswa/Alumni Universitas Negeri Malang

Terakhir diupdate 07 Oktober 2021

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