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Sederhanakan dalam bentuk pangkat positif. (6x3y4xy2​)3×(3x2y−22x3y​)−2

Pertanyaan

Sederhanakan dalam bentuk pangkat positif.

  1. open parentheses fraction numerator 4 x y squared over denominator 6 x cubed y end fraction close parentheses cubed cross times open parentheses fraction numerator 2 x cubed y over denominator 3 x squared y to the power of negative 2 end exponent end fraction close parentheses to the power of negative 2 end exponent

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

 open parentheses fraction numerator 4 x y squared over denominator 6 x cubed y end fraction close parentheses cubed cross times open parentheses fraction numerator 2 x cubed y over denominator 3 x squared y to the power of negative 2 end exponent end fraction close parentheses to the power of negative 2 end exponent equals fraction numerator 2 over denominator 3 x to the power of 8 y cubed 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 4 x y squared over denominator 6 x cubed y end fraction close parentheses cubed cross times open parentheses fraction numerator 2 x cubed y over denominator 3 x squared y to the power of negative 2 end exponent end fraction close parentheses to the power of negative 2 end exponent equals open parentheses 2 over 3 x to the power of 1 minus 3 end exponent y to the power of 2 minus 1 end exponent close parentheses cubed cross times open parentheses 2 over 3 x to the power of 3 minus 2 end exponent y to the power of 1 plus 2 end exponent close parentheses to the power of negative 2 end exponent equals open parentheses 2 over 3 x to the power of negative 2 end exponent y close parentheses cubed cross times open parentheses 2 over 3 x y cubed close parentheses to the power of negative 2 end exponent equals open parentheses begin display style 2 over 3 x to the power of negative 2 end exponent y end style close parentheses cubed over open parentheses begin display style 2 over 3 x y cubed end style close parentheses squared equals fraction numerator open parentheses begin display style 2 over 3 end style close parentheses cubed x to the power of negative 6 end exponent y cubed over denominator open parentheses begin display style 2 over 3 end style close parentheses squared x squared y to the power of 6 end fraction equals open parentheses 2 over 3 close parentheses to the power of 3 minus 2 end exponent x to the power of negative 6 minus 2 end exponent y to the power of 3 minus 6 end exponent equals open parentheses 2 over 3 close parentheses x to the power of negative 8 end exponent y to the power of negative 3 end exponent equals fraction numerator 2 over denominator 3 x to the power of 8 y cubed end fraction


Jadi, open parentheses fraction numerator 4 x y squared over denominator 6 x cubed y end fraction close parentheses cubed cross times open parentheses fraction numerator 2 x cubed y over denominator 3 x squared y to the power of negative 2 end exponent end fraction close parentheses to the power of negative 2 end exponent equals fraction numerator 2 over denominator 3 x to the power of 8 y cubed end fraction.

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