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Pertanyaan

Diketahui begin mathsize 14px style m equals fraction numerator 21 a to the power of negative 3 end exponent b cubed over denominator b c to the power of negative 5 end exponent end fraction end style dan begin mathsize 14px style n equals fraction numerator 49 a to the power of negative 6 end exponent b c to the power of 10 over denominator a to the power of 4 c cubed end fraction end style.Jika begin mathsize 14px style m divided by n equals fraction numerator 3 a to the power of p b to the power of q over denominator 7 c to the power of r end fraction end style, serta begin mathsize 14px style p end style, size 14px q, dan size 14px r berturut-turut merupakan ukuran panjang, lebar, dan tinggi dari sebuah balok, maka volume balok tersebut adalah … satuan volume.

  1. begin mathsize 14px style 21 over 2 end style

  2. size 14px 28 over size 14px 3

  3. begin mathsize 14px style 14 end style

  4. size 14px 27

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row m equals cell fraction numerator 21 a to the power of negative 3 end exponent b cubed over denominator b c to the power of negative 5 end exponent end fraction end cell row blank equals cell 21 a to the power of negative 3 end exponent b to the power of 3 minus 1 end exponent c to the power of 5 end cell row blank equals cell 21 a to the power of negative 3 end exponent b squared c to the power of 5 end cell end table end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row n equals cell fraction numerator 49 a to the power of negative 6 end exponent b c to the power of 10 over denominator a to the power of 4 c cubed end fraction end cell row blank equals cell 49 a to the power of negative 6 minus 4 end exponent b c to the power of 10 minus 3 end exponent end cell row blank equals cell 49 a to the power of negative 10 end exponent b c to the power of 7 end cell end table end style

Maka kita peroleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell m divided by n end cell equals cell 21 a to the power of negative 3 end exponent b squared c to the power of 5 divided by 49 a to the power of negative 10 end exponent b c to the power of 7 end cell row blank equals cell fraction numerator 21 a to the power of negative 3 end exponent b squared c to the power of 5 over denominator 49 a to the power of negative 10 end exponent b c to the power of 7 end fraction end cell row blank equals cell fraction numerator 3 a to the power of negative 3 minus left parenthesis 10 right parenthesis end exponent b to the power of 2 minus 1 end exponent c to the power of 5 minus 7 end exponent over denominator 7 end fraction end cell row blank equals cell fraction numerator 3 a to the power of negative 3 plus 10 end exponent b to the power of 2 minus 1 end exponent c to the power of 5 minus 7 end exponent over denominator 7 end fraction end cell row blank equals cell fraction numerator 3 a to the power of 7 b to the power of 1 c to the power of negative 2 end exponent over denominator 7 end fraction end cell row blank equals cell fraction numerator 3 a to the power of 7 b over denominator 7 c squared end fraction end cell end table end style

Pada soal diketahui begin mathsize 14px style m divided by n equals fraction numerator 3 a to the power of p b to the power of q over denominator 7 c to the power of r end fraction end style, sehingga kita punya

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell m divided by n end cell equals cell fraction numerator 3 a to the power of 7 b over denominator 7 c squared end fraction end cell row cell fraction numerator 3 a to the power of p b to the power of q over denominator 7 c to the power of r end fraction end cell equals cell fraction numerator 3 a to the power of 7 b over denominator 7 c squared end fraction end cell end table end style

Dengan menyamakan pangkat dari begin mathsize 14px style a end stylesize 14px b, dan size 14px c, kita peroleh

begin mathsize 14px style p equals 7 end style, size 14px q size 14px equals size 14px 1, dan size 14px r size 14px equals size 14px 2.

Dengan demikian, volume balok tersebut adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row V equals cell panjang cross times lebar cross times tinggi end cell row blank equals cell p cross times q cross times r end cell row blank equals cell 7 cross times 1 cross times 2 end cell row blank equals 14 end table end style

Jadi, jawaban yang tepat adalah C.

61

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