Roboguru

Sederhanakan o. ​​8x5y42(x2y3)3​​

Pertanyaan

Sederhanakan

o. 8x5y42(x2y3)3  

Pembahasan Soal:

Ingat!

Sifat bilangan berangkat:

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

Sehingga:

8x5y42(x2y3)3=====8x5y42(x2)3(y3)38x5y42x2×3y3×34x5y4x6y941x65y9441xy5

Dengan demikian, bentuk sederhana dari 8x5y42(x2y3)3 adalah 41xy5.

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

Sederhanakanlah a.

Pembahasan Soal:

Ingat kembali sifat-sifat bilangan berpangkat berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell a to the power of m over a to the power of n end cell equals cell a to the power of m minus n end exponent end cell row cell open parentheses a to the power of m close parentheses to the power of n end cell equals cell a to the power of m cross times n end exponent end cell row cell open parentheses a cross times b close parentheses to the power of m end cell equals cell a to the power of m cross times b 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 2 to the power of 4 cross times 3 to the power of 6 over denominator 2 cubed cross times 3 squared end fraction close parentheses cubed end cell equals cell open parentheses 2 to the power of 4 minus 3 end exponent cross times 3 to the power of 6 minus 2 end exponent close parentheses cubed end cell row blank equals cell open parentheses 2 to the power of 1 cross times 3 to the power of 4 close parentheses cubed end cell row blank equals cell open parentheses 2 to the power of 1 close parentheses cubed cross times open parentheses 3 to the power of 4 close parentheses cubed end cell row blank equals cell 2 to the power of 1 cross times 3 end exponent cross times 3 to the power of 4 cross times 3 end exponent end cell row blank equals cell 2 cubed cross times 3 to the power of 12 end cell end table 

Jadi, table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 2 to the power of 4 cross times 3 to the power of 6 over denominator 2 cubed cross times 3 squared end fraction close parentheses cubed end cell equals cell 2 cubed cross times 3 to the power of 12 end cell end table.

0

Roboguru

Bentuk sederhana dari adalah....

Pembahasan Soal:

Ingat kembali:

konsep sifat eksponen:

a to the power of n equals stack stack a cross times a cross times a cross times... cross times a with underbrace below with n below 1 over a to the power of n equals a to the power of negative n end exponent open parentheses a to the power of n close parentheses to the power of m equals a to the power of n times m end exponent a to the power of m over a to the power of n equals a to the power of m minus n end exponent m-th root of a to the power of n end root equals a to the power of n over m end exponent

Sehingga, diperoleh perhitungan:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 81 a to the power of negative 12 end exponent b to the power of 10 c to the power of 5 end root over denominator cube root of negative 27 a to the power of negative 8 end exponent b to the power of 6 end root end fraction end cell equals cell open parentheses 3 to the power of 4 a to the power of negative 12 end exponent b to the power of 10 c to the power of 5 close parentheses to the power of begin display style 1 half end style end exponent over open parentheses open parentheses negative 3 close parentheses cubed a to the power of negative 8 end exponent b to the power of 6 close parentheses to the power of begin display style 1 third end style end exponent end cell row blank equals cell fraction numerator 3 squared a to the power of negative 6 end exponent b to the power of 5 c to the power of begin display style 5 over 2 end style end exponent over denominator open parentheses negative 3 close parentheses a to the power of begin display style fraction numerator negative 8 over denominator 3 end fraction end style end exponent b squared end fraction end cell row blank equals cell negative 3 to the power of 2 minus 1 end exponent a to the power of negative 6 minus fraction numerator negative 8 over denominator 3 end fraction end exponent b to the power of 5 minus 2 end exponent c to the power of 5 over 2 end exponent end cell row blank equals cell negative 3 a to the power of negative 10 over 3 end exponent b cubed c to the power of 5 over 2 end exponent end cell row blank equals cell negative fraction numerator 3 b cubed c to the power of 5 over 2 end exponent over denominator a to the power of 10 over 3 end exponent end fraction end cell end table

Dengan demikian, bentuk sederhana dari bentuk akar tersbut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 b cubed c to the power of 5 over 2 end exponent over denominator a to the power of 10 over 3 end exponent end fraction end cell end table

Jadi, jawaban yang tepat adalah C

0

Roboguru

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:

begin mathsize 14px style fraction numerator a to the power of negative 5 end exponent b to the power of negative 1 end exponent c to the power of negative 4 end exponent over denominator open parentheses a b c close parentheses to the power of negative 6 end exponent end fraction equals fraction numerator a to the power of negative 5 end exponent b to the power of negative 1 end exponent c to the power of negative 4 end exponent over denominator a to the power of negative 6 end exponent b to the power of negative 6 end exponent c to the power of negative 6 end exponent end fraction space space space space space space space space space space space space space space space space space equals a to the power of negative 5 minus open parentheses negative 6 close parentheses end exponent b to the power of negative 1 minus open parentheses negative 6 close parentheses end exponent c to the power of negative 4 minus open parentheses negative 6 close parentheses end exponent space space space space space space space space space space space space space space space space space equals a b to the power of 5 c squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space end style 

Jadi, jawaban yang tepat adalah C

2

Roboguru

b.

Pembahasan Soal:

Bilangan berpangkat bulat positif dapat didefinisikan sebagai berikut.

a to the power of n equals stack a cross times a cross times a cross times horizontal ellipsis cross times a with underbrace below table row blank cell space space space space space space space space end cell cell n space text faktor end text end cell end table

Ingat sifat bilangan berpangkat berikut.

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 n end exponent

open parentheses a b close parentheses to the power of m equals a to the power of m b to the power of m

open parentheses a divided by b close parentheses to the power of m equals a to the power of m divided by b to the power of m comma space b not equal to 0

a to the power of negative m end exponent equals 1 over a to the power of m comma space a not equal to 0

sehingga penyelesaian soal di atas, yaitu

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator open parentheses open parentheses x to the power of begin display style 1 half end style end exponent y to the power of negative begin display style 1 fourth end style end exponent close parentheses to the power of negative begin display style 1 third end style end exponent close parentheses to the power of 12 over denominator x to the power of negative begin display style 1 fifth end style end exponent y to the power of begin display style 1 half end style end exponent end fraction close parentheses to the power of 10 end cell equals cell open parentheses fraction numerator open parentheses open parentheses x to the power of begin display style 1 half end style end exponent close parentheses to the power of negative begin display style 1 third end style end exponent open parentheses y to the power of negative begin display style 1 fourth end style end exponent close parentheses to the power of negative begin display style 1 third end style end exponent close parentheses to the power of 12 over denominator x to the power of negative 1 fifth end exponent y to the power of 1 half end exponent end fraction close parentheses to the power of 10 end cell row blank equals cell open parentheses fraction numerator open parentheses x to the power of negative begin display style 1 over 6 end style end exponent y to the power of begin display style 1 over 12 end style end exponent close parentheses to the power of 12 over denominator x to the power of negative 1 fifth end exponent y to the power of 1 half end exponent end fraction close parentheses to the power of 10 end cell row blank equals cell open parentheses fraction numerator open parentheses x to the power of negative 1 over 6 end exponent close parentheses to the power of 12 open parentheses y to the power of 1 over 12 end exponent close parentheses to the power of 12 over denominator x to the power of negative 1 fifth end exponent y to the power of 1 half end exponent end fraction close parentheses to the power of 10 end cell row blank equals cell open parentheses fraction numerator x to the power of negative 2 end exponent y over denominator x to the power of negative 1 fifth end exponent y to the power of 1 half end exponent end fraction close parentheses to the power of 10 end cell row blank equals cell open parentheses x to the power of negative 2 end exponent y close parentheses to the power of 10 over open parentheses x to the power of negative 1 fifth end exponent y to the power of 1 half end exponent close parentheses to the power of 10 end cell row blank equals cell fraction numerator open parentheses x to the power of negative 2 end exponent close parentheses to the power of 10 open parentheses y close parentheses to the power of 10 over denominator open parentheses x to the power of negative 1 fifth end exponent close parentheses to the power of 10 open parentheses y to the power of 1 half end exponent close parentheses to the power of 10 end fraction end cell row blank equals cell fraction numerator x to the power of negative 20 end exponent y to the power of 10 over denominator x to the power of negative 2 end exponent y to the power of 5 end fraction end cell row blank equals cell x to the power of negative 20 minus open parentheses negative 2 close parentheses end exponent y to the power of 10 minus 5 end exponent end cell row blank equals cell x to the power of negative 18 end exponent y to the power of 5 end cell row blank equals cell y to the power of 5 over x to the power of 18 end cell end table

Dengan demikian, bentuk sederhana dari table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator open parentheses open parentheses x to the power of begin display style 1 half end style end exponent y to the power of negative begin display style 1 fourth end style end exponent close parentheses to the power of negative begin display style 1 third end style end exponent close parentheses to the power of 12 over denominator x to the power of negative begin display style 1 fifth end style end exponent y to the power of begin display style 1 half end style end exponent end fraction close parentheses to the power of 10 end cell equals cell y to the power of 5 over x to the power of 18 end cell end table

0

Roboguru

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