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Diketahui  dan . Bentuk sederhana dari  adalah...

Pertanyaan

Diketahui straight a not equal to 0 comma straight b not equal to 0 comma dan straight c not equal to 0. Bentuk sederhana dari open parentheses fraction numerator 12 straight a to the power of negative 5 end exponent bc over denominator 84 straight a squared straight b to the power of negative 1 end exponent straight c end fraction close parentheses to the power of negative 1 end exponent adalah...

  1. 1 over 7 straight a to the power of 7 straight b squared 

  2. 1 over 7 straight a to the power of negative 7 end exponent straight b squared 

  3. fraction numerator 7 straight a to the power of 7 over denominator straight b squared end fraction  

  4. fraction numerator 7 over denominator straight a to the power of 7 straight b squared end fraction 

Pembahasan Soal:

Sesuai dengan sifat bilangan berpangkat, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 12 straight a to the power of negative 5 end exponent bc over denominator 84 straight a squared straight b to the power of negative 1 end exponent straight c end fraction close parentheses to the power of negative 1 end exponent end cell equals cell open parentheses 1 over 7 straight a to the power of negative 5 minus 2 end exponent straight b to the power of 1 minus open parentheses negative 1 close parentheses end exponent straight c to the power of 1 minus 1 end exponent close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses 1 over 7 straight a to the power of negative 7 end exponent straight b squared straight c to the power of 0 close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses 7 to the power of negative 1 end exponent straight a to the power of negative 7 end exponent straight b squared times 1 close parentheses to the power of negative 1 end exponent end cell row blank equals cell 7 straight a to the power of 7 straight b to the power of negative 2 end exponent end cell row blank equals cell fraction numerator 7 straight a to the power of 7 over denominator straight b squared end fraction end cell end table 

Oleh karena itu, jawaban yang benar adalah C.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

K. Putri

Mahasiswa/Alumni Universitas Pendidikan Ganesha

Terakhir diupdate 02 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Bentuk sederhana dari  adalah ...

Pembahasan Soal:

Mencari bentuk sederhana dari open parentheses fraction numerator p to the power of 5 q to the power of negative 5 end exponent over denominator p to the power of 9 q to the power of negative 1 end exponent end fraction close parentheses to the power of negative 2 end exponent:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator p to the power of 5 q to the power of negative 5 end exponent over denominator p to the power of 9 q to the power of negative 1 end exponent end fraction close parentheses to the power of negative 2 end exponent end cell equals cell 1 over open parentheses fraction numerator p to the power of 5 q to the power of negative 5 end exponent over denominator p to the power of 9 q to the power of negative 1 end exponent end fraction close parentheses squared end cell row blank equals cell fraction numerator 1 over denominator open parentheses fraction numerator p to the power of 10 q to the power of negative 10 end exponent over denominator p to the power of 18 q to the power of negative 2 end exponent end fraction close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator p to the power of negative 8 end exponent q to the power of negative 8 end exponent end fraction end cell row blank equals cell p to the power of 8 q to the power of 8 end cell row blank equals cell open parentheses p q close parentheses to the power of 8 end cell end table  

Jadi, bentuk sederhana dari open parentheses fraction numerator p to the power of 5 q to the power of negative 5 end exponent over denominator p to the power of 9 q to the power of negative 1 end exponent end fraction close parentheses to the power of negative 2 end exponent adalah open parentheses p q close parentheses to the power of 8.

Dengan demikian, jawaban yang tepat adalah A.

0

Roboguru

Bentuk sederhana dari  adalah....

Pembahasan Soal:

Sifat bilangan berpangkat yang digunakan:
1. space open parentheses a to the power of m close parentheses to the power of n equals a to the power of m n end exponent 2. space 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   

Dengan menggunakan sifat operasi bilangan berpangkat diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 4 p to the power of negative 1 end exponent q squared r cubed over denominator 32 p squared q to the power of negative 1 end exponent r to the power of 6 end fraction close parentheses to the power of negative 1 end exponent end cell equals cell fraction numerator 32 p squared q to the power of negative 1 end exponent r to the power of 6 over denominator 4 p to the power of negative 1 end exponent q squared r cubed end fraction end cell row blank equals cell 32 over 4 p to the power of 2 minus open parentheses negative 1 close parentheses end exponent q to the power of negative 1 minus 2 end exponent r to the power of 6 minus 3 end exponent end cell row blank equals cell 8 p cubed q to the power of negative 3 end exponent r cubed end cell end table

Oleh karena itu, jawaban yang benar adalah A.

0

Roboguru

Bentuk sederhana dari  adalah ....

Pembahasan Soal:

Diketahui bentuk eksponen open parentheses fraction numerator a b squared c to the power of negative 3 end exponent over denominator a to the power of negative 3 end exponent b squared c to the power of 4 end fraction close parentheses cubed sehingga dapat ditentukan bentuk sederhananya sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator a b squared c to the power of negative 3 end exponent over denominator a to the power of negative 3 end exponent b squared c to the power of 4 end fraction close parentheses cubed end cell equals cell open parentheses fraction numerator a to the power of 1 plus 3 end exponent b to the power of 2 minus 2 end exponent over denominator c to the power of 4 plus 3 end exponent end fraction close parentheses cubed end cell row blank equals cell open parentheses fraction numerator a to the power of 4 b to the power of 0 over denominator c to the power of 7 end fraction close parentheses cubed end cell row blank equals cell open parentheses a to the power of 4 over c to the power of 7 close parentheses cubed end cell row blank equals cell a to the power of 4 times 3 end exponent over c to the power of 7 times 3 end exponent end cell row blank equals cell a to the power of 12 over c to the power of 21 end cell end table 

Jadi, jawaban yang benar adalah A.

0

Roboguru

Diketahui , dan . Bentuk sederhana dari  adalah ....

Pembahasan Soal:

Ingat kembali:

straight a to the power of straight m over straight a to the power of straight n equals straight a to the power of straight m minus straight n end exponent straight a to the power of negative straight n end exponent equals 1 over straight a to the power of straight n straight a to the power of 0 equals 1 

Diketahui:

open parentheses fraction numerator 12 straight a to the power of negative 5 end exponent bc over denominator 84 straight a squared straight b to the power of negative 1 end exponent straight c end fraction close parentheses to the power of negative 1 end exponent 

Maka:

open parentheses fraction numerator 12 straight a to the power of negative 5 end exponent bc over denominator 84 straight a squared straight b to the power of negative 1 end exponent straight c end fraction close parentheses to the power of negative 1 end exponent equals open parentheses 12 over 84 times straight a to the power of negative 5 minus 2 end exponent times straight b to the power of 1 minus open parentheses negative 1 close parentheses end exponent times straight c to the power of 1 minus 1 end exponent close parentheses to the power of negative 1 end exponent open parentheses fraction numerator 12 straight a to the power of negative 5 end exponent bc over denominator 84 straight a squared straight b to the power of negative 1 end exponent straight c end fraction close parentheses to the power of negative 1 end exponent equals open parentheses 1 over 7 times straight a to the power of negative 7 end exponent times straight b squared times straight c to the power of 0 close parentheses to the power of negative 1 end exponent open parentheses fraction numerator 12 straight a to the power of negative 5 end exponent bc over denominator 84 straight a squared straight b to the power of negative 1 end exponent straight c end fraction close parentheses to the power of negative 1 end exponent equals open parentheses 1 over 7 close parentheses to the power of negative 1 end exponent times open parentheses straight a to the power of negative 7 end exponent close parentheses to the power of negative 1 end exponent times open parentheses straight b squared close parentheses to the power of negative 1 end exponent times open parentheses straight c to the power of 0 close parentheses to the power of negative 1 end exponent open parentheses fraction numerator 12 straight a to the power of negative 5 end exponent bc over denominator 84 straight a squared straight b to the power of negative 1 end exponent straight c end fraction close parentheses to the power of negative 1 end exponent equals 7 times straight a to the power of 7 times straight b to the power of negative 2 end exponent times straight c to the power of 0 open parentheses fraction numerator 12 straight a to the power of negative 5 end exponent bc over denominator 84 straight a squared straight b to the power of negative 1 end exponent straight c end fraction close parentheses to the power of negative 1 end exponent equals 7 times straight a to the power of 7 times 1 over straight b squared times 1 open parentheses fraction numerator 12 straight a to the power of negative 5 end exponent bc over denominator 84 straight a squared straight b to the power of negative 1 end exponent straight c end fraction close parentheses to the power of negative 1 end exponent equals fraction numerator 7 straight a to the power of 7 over denominator straight b squared end fraction 

Jadi, jawaban yang benar adalah D.

1

Roboguru

Bentuk sederhana dari  adalah ....

Pembahasan Soal:

Ingat Kembali:

straight a to the power of straight m space colon space straight b to the power of straight n equals straight a to the power of straight m minus straight n end exponent straight a to the power of negative straight n end exponent equals 1 over straight a to the power of straight n open parentheses straight a to the power of straight m close parentheses to the power of straight n equals straight a to the power of straight m cross times straight n end exponent 

Maka:

open parentheses fraction numerator straight a to the power of 4 straight b to the power of negative 5 end exponent straight c to the power of negative 6 end exponent over denominator straight a to the power of 4 straight b to the power of negative 6 end exponent straight c to the power of negative 5 end exponent end fraction close parentheses cubed equals open parentheses straight a to the power of 4 minus 4 end exponent times straight b to the power of negative 5 minus open parentheses negative 6 close parentheses end exponent times straight c to the power of negative 6 minus open parentheses negative 5 close parentheses end exponent close parentheses cubed space space space space space space space space space space space space space space space space space space space space space equals open parentheses straight a to the power of 0 times straight b to the power of 1 times straight c to the power of negative 1 end exponent close parentheses cubed space space space space space space space space space space space space space space space space space space space space space equals straight a to the power of 0 times straight b cubed times straight c to the power of negative 3 end exponent space space space space space space space space space space space space space space space space space space space space space equals 1 times 1 over straight b to the power of negative 3 end exponent times straight c to the power of negative 3 end exponent space space space space space space space space space space space space space space space space space space space space space equals straight c to the power of negative 3 end exponent over straight b to the power of negative 3 end exponent space space space space space space space space space space space space space space space space space space space space space equals open parentheses straight c over straight b close parentheses to the power of negative 3 end exponent 

Jadi, jawaban yang benar adalah D.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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