Roboguru

Pertanyaan

Sederhanakan dalam bentuk pangkat positif.

  1. open parentheses fraction numerator 2 a cubed b c squared over denominator 3 a squared b to the power of negative 2 end exponent c end fraction close parentheses divided by open parentheses fraction numerator 6 a to the power of 4 b cubed c over denominator 9 a squared b c squared end fraction close parentheses squared

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

 open parentheses fraction numerator 2 a cubed b c squared over denominator 3 a squared b to the power of negative 2 end exponent c end fraction close parentheses divided by open parentheses fraction numerator 6 a to the power of 4 b cubed c over denominator 9 a squared b c squared end fraction close parentheses squared equals fraction numerator 3 c cubed over denominator 2 a cubed b end fraction.

Pembahasan

Ingat kembali beberapa sifat bilangan berpangkat berikut:

  1. 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
  2. a to the power of negative m end exponent equals 1 over a to the power of m
  3. 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 m
  4. a to the power of m over a to the power of n equals a to the power of m minus n end exponent


Sehingga soal tersebut dapat kita hitung sebagai berikut:


open parentheses fraction numerator 2 a cubed b c squared over denominator 3 a squared b to the power of negative 2 end exponent c end fraction close parentheses divided by open parentheses fraction numerator 6 a to the power of 4 b cubed c over denominator 9 a squared b c squared end fraction close parentheses squared equals open parentheses 2 over 3 a to the power of 3 minus 2 end exponent b to the power of 1 plus 2 end exponent c to the power of 2 minus 1 end exponent close parentheses divided by open parentheses 2 over 3 a to the power of 4 minus 2 end exponent b to the power of 3 minus 1 end exponent c to the power of 1 minus 2 end exponent close parentheses squared equals open parentheses 2 over 3 a b cubed c close parentheses divided by open parentheses 2 over 3 a squared b squared c to the power of negative 1 end exponent close parentheses squared equals fraction numerator open parentheses begin display style 2 over 3 a b cubed c end style close parentheses over denominator open parentheses begin display style 2 over 3 a squared b squared c to the power of negative 1 end exponent end style close parentheses squared end fraction equals fraction numerator open parentheses begin display style 2 over 3 end style close parentheses a b cubed c over denominator open parentheses begin display style 2 over 3 end style close parentheses squared a to the power of 4 b to the power of 4 c to the power of negative 2 end exponent end fraction equals open parentheses 2 over 3 close parentheses to the power of 1 minus 2 end exponent a to the power of 1 minus 4 end exponent b to the power of 3 minus 4 end exponent c to the power of 1 plus 2 end exponent equals open parentheses 2 over 3 close parentheses to the power of negative 1 end exponent a to the power of negative 3 end exponent b to the power of negative 1 end exponent c cubed equals fraction numerator 3 c cubed over denominator 2 a cubed b end fraction


Jadi, open parentheses fraction numerator 2 a cubed b c squared over denominator 3 a squared b to the power of negative 2 end exponent c end fraction close parentheses divided by open parentheses fraction numerator 6 a to the power of 4 b cubed c over denominator 9 a squared b c squared end fraction close parentheses squared equals fraction numerator 3 c cubed over denominator 2 a cubed b end fraction.

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