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Bentuk sederhana dari ​​(p.q−2)2(p3.q−2)2​​ adalah …

Pertanyaan

Bentuk sederhana dari (p.q2)2(p3.q2)2 adalah …

  1. p3

  2. p4

  3.  q2

  4. q4

  5. p2.q4

Pembahasan Soal:

Ingat!

Sifat bilangan berangkat:  

  • (a×b)n=an×bn 
  • (am)n=am×n   
  • am:an=amn 

Sehingga:

(p.q2)2(p3.q2)2=======(p)2.(q2)2(p3)2.(q2)2p2.q2×2p3×2.q2×2p2.q4p6.q4p62.q4(4)p4.q0p4.1p4 

Oleh karena itu, jawaban yang tepat adalah B.

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

Nilai  adalah ...

Pembahasan Soal:

Ingat kembali beberapa sifat bilangan berpangkat berikut:

  1. 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
  2. a to the power of negative m end exponent equals 1 over a to the power of m
  3. 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
  4. 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
  5. a to the power of m over a to the power of n equals a to the power of m minus n end exponent


Sehingga soal tersebut dapat kita hitung sebagai berikut:


table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 8 to the power of negative 2 end exponent cross times 24 to the power of 4 over denominator 36 to the power of 5 cross times 256 to the power of negative 1 end exponent end fraction end cell equals cell fraction numerator open parentheses 2 cubed close parentheses to the power of negative 2 end exponent cross times open parentheses 2 cubed cross times 3 close parentheses to the power of 4 over denominator open parentheses 2 squared cross times 3 squared close parentheses to the power of 5 cross times open parentheses 2 to the power of 8 close parentheses to the power of negative 1 end exponent end fraction end cell row blank equals cell fraction numerator 2 to the power of negative 6 end exponent cross times 2 to the power of 12 cross times 3 to the power of 4 over denominator 2 to the power of 10 cross times 3 to the power of 10 cross times 2 to the power of negative 8 end exponent end fraction end cell row blank equals cell fraction numerator 2 to the power of 12 minus 6 end exponent cross times 3 to the power of 4 over denominator 2 to the power of 10 minus 8 end exponent cross times 3 to the power of 10 end fraction end cell row blank equals cell fraction numerator 2 to the power of 6 cross times 3 to the power of 4 over denominator 2 squared cross times 3 to the power of 10 end fraction end cell row blank equals cell 2 to the power of 6 minus 2 end exponent cross times 3 to the power of 4 minus 10 end exponent end cell row blank equals cell 2 to the power of 4 cross times 3 to the power of negative 6 end exponent end cell row blank equals cell 2 to the power of 4 over 3 to the power of 6 end cell row blank equals cell 16 over 729 end cell end table


Jadi, fraction numerator 8 to the power of negative 2 end exponent cross times 24 to the power of 4 over denominator 36 to the power of 5 cross times 256 to the power of negative 1 end exponent end fraction equals 16 over 729.

Oleh karena itu, jawaban yang benar adalah E.

0

Roboguru

disederhanakan menjadi

Pembahasan Soal:

Diketahui fraction numerator 8 m to the power of 5 n to the power of 4 over denominator open parentheses 2 m n to the power of negative 2 end exponent close parentheses cubed end fraction maka berdasarkan sifat bilangan berpangkat 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 maka diperoleh

fraction numerator 8 m to the power of 5 n to the power of 4 over denominator open parentheses 2 m n to the power of negative 2 end exponent close parentheses cubed end fraction equals fraction numerator 8 m to the power of 5 n to the power of 4 over denominator 2 cubed m cubed open parentheses n to the power of negative 2 end exponent close parentheses cubed end fraction

Berdasarkan sifat bilangan berpangkat yaitu 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 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 8 m to the power of 5 n to the power of 4 over denominator open parentheses 2 m n to the power of negative 2 end exponent close parentheses cubed end fraction end cell equals cell fraction numerator 8 m to the power of 5 n to the power of 4 over denominator 2 cubed m cubed open parentheses n to the power of negative 2 end exponent close parentheses cubed end fraction end cell row blank equals cell fraction numerator up diagonal strike 8 m to the power of 5 n to the power of 4 over denominator up diagonal strike 8 m cubed n to the power of negative 2 cross times 3 end exponent end fraction end cell row blank equals cell fraction numerator m to the power of 5 n to the power of 4 over denominator m cubed n to the power of negative 6 end exponent end fraction end cell end table

Berdasarkan sifat bilangan berpangkat yaitu 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 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 8 m to the power of 5 n to the power of 4 over denominator open parentheses 2 m n to the power of negative 2 end exponent close parentheses cubed end fraction end cell equals cell fraction numerator 8 m to the power of 5 n to the power of 4 over denominator 2 cubed m cubed open parentheses n to the power of negative 2 end exponent close parentheses cubed end fraction end cell row blank equals cell fraction numerator up diagonal strike 8 m to the power of 5 n to the power of 4 over denominator up diagonal strike 8 m cubed n to the power of negative 2 cross times 3 end exponent end fraction end cell row blank equals cell fraction numerator m to the power of 5 n to the power of 4 over denominator m cubed n to the power of negative 6 end exponent end fraction end cell row blank equals cell m to the power of 5 minus 3 end exponent n to the power of 4 minus open parentheses negative 6 close parentheses end exponent end cell row blank equals cell m squared n to the power of 4 plus 6 end exponent end cell row blank equals cell m squared n to the power of 10 end cell end table

Jadi fraction numerator 8 m to the power of 5 n to the power of 4 over denominator open parentheses 2 m n to the power of negative 2 end exponent close parentheses cubed end fraction disederhanakan menjadi m squared n to the power of 10.

Oleh karena itu, jawaban yang benar adalah C.

2

Roboguru

Bentuk sederhana dari  adalah ...

Pembahasan Soal:

Mencari bentuk sederhana dari open parentheses fraction numerator 12 a cubed b squared over denominator 4 a b to the power of 5 end fraction close parentheses to the power of negative 1 end exponent:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 12 a cubed b squared over denominator 4 a b to the power of 5 end fraction close parentheses to the power of negative 1 end exponent end cell equals cell open parentheses 12 over 4 times fraction numerator a cubed b squared over denominator a b to the power of 5 end fraction close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses 3 times a to the power of 3 minus 1 end exponent b to the power of 2 minus 5 end exponent close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses 3 a squared b to the power of negative 3 end exponent close parentheses to the power of negative 1 end exponent end cell row blank equals cell 3 to the power of negative 1 end exponent a to the power of negative 2 end exponent b cubed end cell row blank equals cell fraction numerator b cubed over denominator 3 a squared end fraction end cell end table 

Jadi, bentuk sederhana dari open parentheses fraction numerator 12 a cubed b squared over denominator 4 a b to the power of 5 end fraction close parentheses to the power of negative 1 end exponent adalah fraction numerator b cubed over denominator 3 a squared end fraction.

Dengan demikian, jawaban yang tepat adalah A.

0

Roboguru

Dengan menggunakan sifat bilangan berpangkat, nyatakan setiap operasi bilangan berikut dalam bentuk . g.

Pembahasan Soal:

Untuk menyatakan ke dalam bentuk a to the power of n  maka dapat dilakukan dengan cara, sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 18 cubed divided by 3 to the power of 6 end cell equals cell open parentheses 2 cross times 3 squared close parentheses cubed divided by 3 to the power of 6 end cell row blank equals cell 2 cubed cross times open parentheses 3 squared close parentheses cubed divided by 3 to the power of 6 end cell row blank equals cell 2 cubed cross times 3 to the power of 6 divided by 3 to the power of 6 end cell row blank equals cell 2 cubed cross times 3 to the power of 6 minus 6 end exponent end cell row blank equals cell 2 cubed cross times 1 end cell row cell space space space space space space space space space space space space space space end cell equals cell 2 cubed end cell end table 

Dengan demikian, bentuk a to the power of n dari operasi bilangan 18 cubed divided by 3 to the power of 6 adalah 2 cubed.

0

Roboguru

Bentuk sederhana  adalah ...

Pembahasan Soal:

Ingat sifat bilangan berpangkat:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses x y close parentheses to the power of n end cell equals cell x to the power of n y to the power of n end cell row cell open parentheses x to the power of m close parentheses to the power of n end cell equals cell x to the power of m n end exponent end cell row cell x to the power of m over x to the power of n end cell equals cell x to the power of m minus n end exponent end cell row cell x to the power of negative m end exponent end cell equals cell 1 over x to the power of m end cell row cell open parentheses x over y close parentheses to the power of m end cell equals cell x to the power of m over y to the power of m end cell end table   

maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 4 x squared y to the power of negative 4 end exponent over denominator 6 x to the power of negative 3 end exponent y to the power of negative 5 end exponent end fraction close parentheses to the power of negative 3 end exponent end cell equals cell fraction numerator 4 to the power of negative 3 end exponent x to the power of 2 open parentheses negative 3 close parentheses end exponent y to the power of negative 4 open parentheses negative 3 close parentheses end exponent over denominator 6 to the power of negative 3 end exponent x to the power of negative 3 open parentheses negative 3 close parentheses end exponent y to the power of negative 5 open parentheses negative 3 close parentheses end exponent end fraction end cell row blank equals cell fraction numerator open parentheses 2 squared close parentheses to the power of negative 3 end exponent x to the power of negative 6 end exponent y to the power of 12 over denominator open parentheses 2 cross times 3 close parentheses to the power of negative 3 end exponent x to the power of 9 y to the power of 15 end fraction end cell row blank equals cell fraction numerator 2 to the power of 2 open parentheses negative 3 close parentheses end exponent x to the power of negative 6 end exponent y to the power of 12 over denominator 2 to the power of negative 3 end exponent times 3 to the power of negative 3 end exponent x to the power of 9 y to the power of 15 end fraction end cell row blank equals cell fraction numerator 2 to the power of negative 6 end exponent x to the power of negative 6 end exponent y to the power of 12 over denominator 2 to the power of negative 3 end exponent times 3 to the power of negative 3 end exponent x to the power of 9 y to the power of 15 end fraction end cell row blank equals cell open parentheses 2 to the power of negative 6 end exponent over 2 to the power of negative 3 end exponent close parentheses open parentheses 1 over 3 to the power of negative 3 end exponent close parentheses open parentheses x to the power of negative 6 end exponent over x to the power of 9 close parentheses open parentheses y to the power of 12 over y to the power of 15 close parentheses end cell row blank equals cell 2 to the power of negative 6 minus open parentheses negative 3 close parentheses end exponent times 3 cubed times x to the power of negative 6 minus 9 end exponent times y to the power of 12 minus 15 end exponent end cell row blank equals cell 2 to the power of negative 3 end exponent times 3 cubed times x to the power of negative 15 end exponent times y to the power of negative 3 end exponent end cell row blank equals cell fraction numerator 3 cubed over denominator 2 cubed x to the power of 15 y cubed end fraction end cell row blank equals cell fraction numerator 27 over denominator 8 x to the power of 15 y cubed end fraction end cell end table  

Bentuk sederhana open parentheses fraction numerator 4 x squared y to the power of negative 4 end exponent over denominator 6 x to the power of negative 3 end exponent y to the power of negative 5 end exponent end fraction close parentheses to the power of negative 3 end exponent adalah fraction numerator 27 over denominator 8 x to the power of 15 y cubed end fraction.

Oleh karena itu, jawaban yang benar adalah E. 

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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