Roboguru

Bentuk sederhana dari  adalah ...

Pertanyaan

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 ...

  1. open parentheses p q close parentheses to the power of 8 

  2. open parentheses p q close parentheses to the power of 4 

  3. p q 

  4. open parentheses p q close parentheses to the power of negative 2 end exponent 

  5. open parentheses p q close parentheses to the power of negative 8 end exponent 

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.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Yoga

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 30 April 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Dengan menggunakan tanda , atau  nyatakan perbandingan masing-masing bilangan berikut. f.

Pembahasan Soal:

Kita akan menentukan hubungan 1 over 3 to the power of 100 space... space 1 over 4 to the power of 100 dengan menggunakan pemisalan sebagai berikut :

1 over a to the power of n...1 over left parenthesis a plus 1 right parenthesis to the power of n

kita misalkan a equals 2 space & space n equals 3, maka diperoleh:

table attributes columnalign right center left columnspacing 2px end attributes row cell 1 over 2 cubed end cell cell... end cell cell 1 over left parenthesis 2 plus 1 right parenthesis cubed end cell row cell 1 over 2 cubed end cell cell... end cell cell 1 over 3 cubed end cell row cell 1 over 8 end cell cell... end cell cell 1 over 27 end cell row cell 1 over 8 end cell greater than cell 1 over 27 end cell end table

sedemikian sehingga : 

1 over a to the power of n greater than 1 over left parenthesis a plus 1 right parenthesis to the power of n,

Jika a equals 3 space & space n equals 100, maka diperoleh:

table attributes columnalign right center left columnspacing 2px end attributes row cell 1 over 3 to the power of 100 end cell greater than cell 1 over left parenthesis 3 plus 1 right parenthesis to the power of 100 end cell row cell 1 over 3 to the power of 100 end cell greater than cell 1 over 4 to the power of 100 end cell end table

Jadi, table attributes columnalign right center left columnspacing 2px end attributes row cell 1 over 3 to the power of 100 end cell greater than cell 1 over 4 to the power of 100 end cell end table.

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Roboguru

Dengan menggunakan tanda , atau  nyatakan perbandingan masing-masing bilangan berikut. g.

Pembahasan Soal:

Untuk mengetahui hubungan 2 comma 713 to the power of 3 comma 14 end exponent space... space 3 comma 14 to the power of 2 comma 713 end exponent, maka kita menggunakan pemisalan sebagai berikut:

a to the power of b... b to the power of a comma space S y a r a t space a less than b

Kita misalkan a equals 4 space d a n space b equals 5, maka diperoleh:

table attributes columnalign right center left columnspacing 2px end attributes row cell 4 to the power of 5 end cell cell... end cell cell 5 to the power of 4 end cell row cell 1.024 end cell cell... end cell 625 row cell 1.024 end cell greater than 625 end table

Sedemikian sehingga:

a to the power of b greater than b to the power of a comma space s y a r a t space a less than b

Jika a equals 2 comma 713 space & space b equals 3 comma 14 maka diperoleh:

2 comma 713 to the power of 3 comma 14 end exponent greater than 3 comma 14 to the power of 2 comma 713 end exponent dengan 2 comma 713 space less than space 3 comma 14.

Jadi, 2 comma 713 to the power of 3 comma 14 end exponent greater than 3 comma 14 to the power of 2 comma 713 end exponent.

1

Roboguru

Bentuk sederhana dari  adalah ...

Pembahasan Soal:

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 open parentheses fraction numerator p to the power of 5 times left parenthesis negative 2 right parenthesis end exponent times q to the power of left parenthesis negative 5 right parenthesis times left parenthesis negative 2 right parenthesis end exponent over denominator p to the power of 9 times left parenthesis negative 2 right parenthesis end exponent times q to the power of left parenthesis negative 1 right parenthesis times left parenthesis negative 2 right parenthesis end exponent end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator p to the power of negative 10 end exponent times q to the power of 10 over denominator p to the power of negative 18 end exponent times q squared end fraction close parentheses end cell row blank equals cell open parentheses p to the power of left parenthesis negative 10 right parenthesis plus 18 end exponent times q to the power of 10 minus 2 end exponent close parentheses end cell row blank equals cell open parentheses p to the power of 8 times q to the power of 8 close parentheses end cell row blank equals cell open parentheses p times q close parentheses to the power of 8 end cell end table


Oleh karena itu, jawaban yang benar adalah A.

0

Roboguru

Sebutkan sifat-sifat eksponen.

Pembahasan Soal:

Sifat-sifat eksponen atau bilangan berpangkat diantaranya sebagai berikut:

  • a to the power of m cross times a to the power of n equals a to the power of m plus n end exponent 
  • 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 
  • 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 
  • 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 
  • open parentheses a over b close parentheses to the power of m equals a to the power of m over b to the power of m 
  • 1 over a to the power of m equals a to the power of negative m end exponent 
  • n-th root of a to the power of m end root equals a to the power of m over n end exponent 
  • a to the power of 0 equals 1 
  • 1 to the power of m equals 1 

Dengan demikian, diperoleh sifat-sifat eksponen seperti di atas.

1

Roboguru

Nyatakanlah bilangan berikut dalam pangkat positif. a.

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 cubed cross times 4 to the power of negative 5 end exponent end cell equals cell 4 to the power of 3 minus 5 end exponent end cell row blank equals cell 4 to the power of negative 2 end exponent end cell row blank equals cell 1 over 4 squared end cell row blank equals cell 1 over 2 to the power of 4 end cell row blank equals cell 1 over 16 end cell end table 

Jadi, bilangan tersebut dalam pangkat positif adalah 1 over 2 to the power of 4 space atau space 1 over 16.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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