Roboguru

Jika a=2 dan b=3, tentukan nilai dari : b. ​​(a−b)−3.(b−aa+b​)−2.(a+b)−31​​

Pertanyaan

Jika a=2 dan b=3, tentukan nilai dari :

b. (ab)3.(baa+b)2.(a+b)31

Pembahasan Soal:

Ingat!

Sifat bilangan berangkat:

  • an=an1     

Sehingga:

=======(ab)3.(baa+b)2.(a+b)31(23)3.(322+3)2.(2+3)31(1)3.(15)2.531(1)31.521.5311(1)31.521.15311.251.11251.251.1255 

Dengan demikian, nilai dari (ab)3.(baa+b)2.(a+b)31 adalah 5

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Sutiawan

Mahasiswa/Alumni Universitas Pasundan

Terakhir diupdate 30 Agustus 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

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.

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

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:

Ingat kembali:

straight a to the power of straight m space colon space 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 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 straight a squared straight b close parentheses cubed space colon space open parentheses straight a squared straight b to the power of 4 close parentheses equals open parentheses straight a squared close parentheses cubed times straight b cubed space colon space straight a squared times straight b to the power of 4 open parentheses straight a squared straight b close parentheses cubed space colon space open parentheses straight a squared straight b to the power of 4 close parentheses equals straight a to the power of 6 times straight b cubed space colon space straight a squared times straight b to the power of 4 open parentheses straight a squared straight b close parentheses cubed space colon space open parentheses straight a squared straight b to the power of 4 close parentheses equals straight a to the power of 6 minus 2 end exponent times straight b to the power of 3 minus 4 end exponent open parentheses straight a squared straight b close parentheses cubed space colon space open parentheses straight a squared straight b to the power of 4 close parentheses equals straight a to the power of 4 times straight b to the power of negative 1 end exponent open parentheses straight a squared straight b close parentheses cubed space colon space open parentheses straight a squared straight b to the power of 4 close parentheses equals straight a to the power of 4 times 1 over straight b open parentheses straight a squared straight b close parentheses cubed space colon space open parentheses straight a squared straight b to the power of 4 close parentheses equals straight a to the power of 4 over straight b 

Jadi, jawaban yang benar adalah B.

0

Roboguru

Sederhanakan bentuk-bentuk berikut! 8a−3b5a−6b8​

Pembahasan Soal:

Ingat kembali sifat bilangan berpangkat berikut.

am÷anam==amnam1,a=0

Sehingga, diperoleh perhitungan:

8a3b5a6b8===8a6(3)b858a3b38a3b3

Jadi, bentuk sederhana dari 8a3b5a6b8 adalah8a3b3.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

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