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Pertanyaan

Nilai dari begin mathsize 14px style 10 to the power of negative 3 end exponent plus 10 to the power of negative 2 end exponent plus 10 to the power of negative 1 end exponent equals.... end style 

  1. begin mathsize 14px style 0 comma 111 end style 

  2. begin mathsize 14px style 1 comma 11 end style  

  3. begin mathsize 14px style 1 comma 21 end style 

  4. begin mathsize 14px style 11 comma 1 end style 

Pembahasan Soal:

Ingat sifat pada bilangan berpangkat yaitu a to the power of negative m end exponent equals 1 over a to the power of m, dari sifat tersebut maka akan didapatkan hasil sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 10 to the power of negative 3 end exponent plus 10 to the power of negative 2 end exponent plus 10 to the power of negative 1 end exponent end cell equals cell 1 over 10 cubed plus 1 over 10 squared plus 1 over 10 to the power of 1 end cell row blank equals cell 1 over 1000 plus 1 over 100 plus 1 over 10 end cell row blank equals cell 0 comma 001 plus 0 comma 01 plus 0 comma 1 end cell row blank equals cell 0 comma 111 end cell end table

Didapatkan hasil yaitu 0 comma 111.

Jadi, jawaban yang tepat adalah A.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

M. Iqbal

Mahasiswa/Alumni Universitas Negeri Semarang

Terakhir diupdate 11 Agustus 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

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

Jika  dan , nilai  adalah ....

Pembahasan Soal:

Sifat bilangan berpangkatan yang digunakan:
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 

Dengan menerapkan sifat pemangkatan bilangan berpangkat, diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 5 to the power of 10 x end exponent end cell equals 1600 row cell 5 to the power of 2 times 5 x end exponent end cell equals 1600 row cell open parentheses 5 to the power of 5 x end exponent close parentheses squared end cell equals 1600 row cell square root of open parentheses 5 to the power of 5 x end exponent close parentheses squared end root end cell equals cell square root of 1600 end cell row cell 5 to the power of 5 x end exponent end cell equals 40 end table end style 

Selanjutnya, dengan menerapkan sifat-sifat bilangan berpangkat, diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 5 to the power of x minus 1 end exponent close parentheses to the power of 5 over 8 to the power of open parentheses negative square root of y close parentheses end exponent end cell equals cell 5 to the power of 5 open parentheses x minus 1 close parentheses end exponent over open parentheses 2 cubed close parentheses to the power of negative square root of y end exponent end cell row blank equals cell 5 to the power of 5 x minus 5 end exponent over 2 to the power of negative 3 square root of y end exponent end cell row blank equals cell fraction numerator begin display style 5 to the power of 5 x end exponent over 5 to the power of 5 end style over denominator begin display style 1 over 2 to the power of 3 square root of y end exponent end style end fraction end cell row blank equals cell 5 to the power of 5 x end exponent over 5 to the power of 5 cross times 2 to the power of 3 square root of y end exponent end cell row blank equals cell 5 to the power of 5 x end exponent over 5 to the power of 5 cross times open parentheses 2 to the power of square root of y end exponent close parentheses cubed end cell row blank equals cell 40 over 5 to the power of 5 cross times 25 cubed end cell row blank equals cell 40 over 5 to the power of 5 cross times open parentheses 5 squared close parentheses cubed end cell row blank equals cell 40 over 5 to the power of 5 cross times 5 to the power of 2 times 3 end exponent end cell row blank equals cell 40 over 5 to the power of 5 cross times 5 to the power of 6 end cell row blank equals cell 40 cross times 5 to the power of 6 minus 5 end exponent end cell row blank equals cell 40 cross times 5 to the power of 1 end cell row blank equals cell 40 cross times 5 end cell row blank equals 200 end table end style 

Jadi, nilai begin mathsize 14px style open parentheses 5 to the power of x minus 1 end exponent close parentheses to the power of 5 over 8 to the power of open parentheses negative square root of y close parentheses end exponent end style adalah 200.

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Roboguru

Diketahui  dan , bentuk sederhana  adalah ...

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses fraction numerator 27 straight x to the power of negative 5 end exponent straight y to the power of negative 3 end exponent over denominator 3 to the power of 5 straight x to the power of negative 7 end exponent straight y to the power of negative 5 end exponent end fraction close parentheses to the power of negative 1 end exponent end cell equals cell open parentheses 3 cubed over 3 to the power of 5 times straight x to the power of negative 5 minus open parentheses negative 7 close parentheses end exponent times straight y to the power of negative 3 minus open parentheses negative 5 close parentheses end exponent close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses 3 to the power of 3 minus 5 end exponent times straight x squared times straight y squared close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses 3 to the power of negative 2 end exponent times straight x squared times straight y squared close parentheses to the power of negative 1 end exponent end cell row blank equals cell 3 squared times straight x to the power of negative 2 end exponent times straight y to the power of negative 2 end exponent end cell row blank equals cell fraction numerator 9 over denominator straight x squared times straight y squared end fraction end cell row blank equals cell 9 over open parentheses xy close parentheses squared end cell end table end style 
 

Jadi, jawaban yang benar adalah E

0

Roboguru

Bentuk sederhana dari  adalah ....

Pembahasan Soal:

Ingatlah sifat-sifat bilangan berpangkat berikut.

left parenthesis straight i right parenthesis space 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 left parenthesis ii right parenthesis space 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

Berdasarkan sifat-sifat di atas, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight a to the power of 4 straight b to the power of negative 3 end exponent straight c squared close parentheses to the power of negative 1 end exponent over open parentheses straight a to the power of negative 3 end exponent straight b to the power of 4 straight c cubed close parentheses squared end cell equals cell fraction numerator straight a to the power of 4 cross times open parentheses negative 1 close parentheses end exponent straight b to the power of open parentheses negative 3 close parentheses cross times open parentheses negative 1 close parentheses end exponent straight c to the power of 2 cross times open parentheses negative 1 close parentheses end exponent over denominator straight a to the power of open parentheses negative 3 close parentheses cross times 2 end exponent straight b to the power of 4 cross times 2 end exponent straight c to the power of 3 cross times 2 end exponent end fraction end cell row blank equals cell fraction numerator straight a to the power of negative 4 end exponent straight b cubed straight c to the power of negative 2 end exponent over denominator straight a to the power of negative 6 end exponent straight b to the power of 8 straight c to the power of 6 end fraction end cell row blank equals cell straight a to the power of negative 4 minus open parentheses negative 6 close parentheses end exponent straight b to the power of 3 minus 8 end exponent straight c to the power of open parentheses negative 2 close parentheses minus 6 end exponent end cell row blank equals cell straight a to the power of negative 4 plus 6 end exponent straight b to the power of negative 5 end exponent straight c to the power of negative 8 end exponent end cell row blank equals cell straight a squared straight b to the power of negative 5 end exponent straight c to the power of negative 8 end exponent end cell row blank equals cell fraction numerator straight a squared over denominator straight b to the power of 5 straight c to the power of 8 end fraction. end cell end table

Dengan demikian, bentuk sederhana dari open parentheses straight a to the power of 4 straight b to the power of negative 3 end exponent straight c squared close parentheses to the power of negative 1 end exponent over open parentheses straight a to the power of negative 3 end exponent straight b to the power of 4 straight c cubed close parentheses squared adalah fraction numerator straight a squared over denominator straight b to the power of 5 straight c to the power of 8 end fraction.

0

Roboguru

Sederhanakan bentuk dibawah ini: e.  ...

Pembahasan Soal:

Menyederhanakan bentuk:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 3 to the power of 5 over 3 to the power of negative 1 end exponent end cell equals cell 3 to the power of 5 minus left parenthesis negative 1 right parenthesis end exponent space end cell row blank equals cell 3 to the power of 5 plus 1 end exponent end cell row blank equals cell 3 to the power of 6 end cell end table end style 

Jadi, bentuk sederhananya adalah begin mathsize 14px style 3 to the power of 6 end style.

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Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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