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Pertanyaan

Bentuk sederhana dari open parentheses fraction numerator 27 a to the power of negative 5 end exponent b to the power of negative 3 end exponent over denominator 3 to the power of 5 a to the power of negative 7 end exponent b to the power of negative 5 end exponent end fraction close parentheses to the power of negative 1 end exponent adalah ...space

  1. 3 squared a squared b squared 

  2. 3 a squared b squared 

  3. 9 a squared b squared 

  4. fraction numerator 3 over denominator a squared b squared end fraction 

  5. fraction numerator 9 over denominator a squared b squared end fraction 

Pembahasan Video:

Pembahasan Soal:

Ingat!

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

Bentuk sederhana dari open parentheses fraction numerator 27 a to the power of negative 5 end exponent b to the power of negative 3 end exponent over denominator 3 to the power of 5 a to the power of negative 7 end exponent b to the power of negative 5 end exponent end fraction close parentheses to the power of negative 1 end exponent adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 27 a to the power of negative 5 end exponent b to the power of negative 3 end exponent over denominator 3 to the power of 5 a to the power of negative 7 end exponent b to the power of negative 5 end exponent end fraction close parentheses to the power of negative 1 end exponent end cell equals cell fraction numerator 3 to the power of 5 a to the power of negative 7 end exponent b to the power of negative 5 end exponent over denominator 3 cubed a to the power of negative 5 end exponent b to the power of negative 3 end exponent end fraction end cell row blank equals cell 3 to the power of 5 minus 3 end exponent a to the power of negative 7 plus 5 end exponent b to the power of negative 5 plus 3 end exponent end cell row blank equals cell 9 a to the power of negative 2 end exponent b to the power of negative 2 end exponent end cell row blank equals cell fraction numerator 9 over denominator a squared b squared end fraction end cell end table 

Dengan demikian, (35a7b527a5b3)1=a2b29.

Oleh karena itu, jawaban yang benar adalah E.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Dwi

Terakhir diupdate 13 September 2021

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Pembahasan Soal:

Untuk soal persamaan eksponen tersebut berlaku sifat-sifat berikut:

  • a to the power of p over a to the power of q equals a to the power of p minus q end exponent dengan a not equal to 0 
  • a to the power of negative m end exponent equals 1 over a to the power of m dengan a not equal to 0 

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x to the power of 4 y to the power of negative 6 end exponent z to the power of negative 3 end exponent over denominator x cubed y to the power of negative 3 end exponent z cubed end fraction end cell equals cell x to the power of 4 minus 3 end exponent y to the power of negative 6 minus open parentheses negative 3 close parentheses end exponent z to the power of negative 3 minus 3 end exponent end cell row blank equals cell x to the power of 1 y to the power of negative 6 plus 3 end exponent z to the power of negative 6 end exponent end cell row blank equals cell x y to the power of negative 3 end exponent z to the power of negative 6 end exponent end cell row blank equals cell fraction numerator x over denominator y cubed z to the power of 6 end fraction end cell end table 

Dengan demikian, bentuk sederhana dari fraction numerator x to the power of 4 y to the power of negative 6 end exponent z to the power of negative 3 end exponent over denominator x cubed y to the power of negative 3 end exponent z cubed end fraction adalah fraction numerator x over denominator y cubed z to the power of 6 end fraction.

0

Roboguru

Pembahasan Soal:

Ingat kembali:

open parentheses a to the power of m close parentheses to the power of n equals a to the power of m times n 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 comma space a not equal to 0

open parentheses a times b close parentheses to the power of n equals a to the power of n times b to the power of n

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 diperoleh perhitungan:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator a to the power of negative 4 end exponent times b squared times c over denominator a times b to the power of negative 6 end exponent times c cubed end fraction close parentheses to the power of 4 end cell equals cell open parentheses a to the power of negative 4 minus 1 end exponent times b to the power of 2 minus open parentheses negative 6 close parentheses end exponent times c to the power of 1 minus 3 end exponent close parentheses to the power of 4 end cell row blank equals cell open parentheses a to the power of negative 5 end exponent times b to the power of 2 plus 6 end exponent times c to the power of negative 2 end exponent close parentheses to the power of 4 end cell row blank equals cell open parentheses a to the power of negative 5 end exponent times b to the power of 8 times c to the power of negative 2 end exponent close parentheses to the power of 4 end cell row blank equals cell open parentheses a to the power of negative 5 end exponent close parentheses to the power of 4 times open parentheses b to the power of 8 close parentheses to the power of 4 times open parentheses c to the power of negative 2 end exponent close parentheses to the power of 4 end cell row blank equals cell a to the power of open parentheses negative 5 close parentheses times 4 end exponent times b to the power of 8 times 4 end exponent times c to the power of open parentheses negative 2 close parentheses times 4 end exponent end cell row blank equals cell a to the power of negative 20 end exponent times b to the power of 32 times c to the power of negative 8 end exponent end cell row blank equals cell fraction numerator b to the power of 32 over denominator a to the power of 20 times c to the power of 8 end fraction end cell end table  


Dengan demikian, hasil dari open parentheses fraction numerator a to the power of negative 4 end exponent times b squared times c over denominator a times b to the power of negative 6 end exponent times c cubed end fraction close parentheses to the power of 4  adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator b to the power of 32 over denominator a to the power of 20 times c to the power of 8 end fraction end cell end table.

Jadi, jawaban yang tepat adalah D.

1

Roboguru

Pembahasan Soal:

Ingat kembali:

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 a space s e b a n y a k space n below comma space a not equal to 0

a to the power of m over a to the power of n equals a to the power of m minus n end exponent comma space a not equal to 0

open parentheses a over b close parentheses to the power of n equals a to the power of n over b to the power of n comma space a not equal to 0 comma space b not equal to 0 

a to the power of m times a to the power of n equals a to the power of m plus n end exponent. space a not equal to 0 

a to the power of 0 equals 1 comma space a not equal to 0

Sehingga, kita peroleh perhitungan:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 2 over 3 close parentheses squared times open parentheses negative 3 over 4 close parentheses squared minus 3 over 2 cubed colon 5 over 8 end cell equals cell 2 squared over 3 squared times open parentheses 3 over 4 close parentheses squared minus 3 over 2 cubed colon 5 over 2 cubed end cell row blank equals cell 2 squared over 3 squared times 3 squared over 4 squared minus fraction numerator 3 over denominator up diagonal strike 2 cubed end strike end fraction times fraction numerator up diagonal strike 2 cubed end strike over denominator 5 end fraction end cell row blank equals cell 2 squared over 3 squared times 3 squared over open parentheses 2 squared close parentheses squared minus 3 over 5 end cell row blank equals cell 2 squared over 3 squared times 3 squared over 2 to the power of 2 times 2 end exponent minus 3 over 5 end cell row blank equals cell 2 squared over 3 squared times 3 squared over 2 to the power of 4 minus 3 over 5 end cell row blank equals cell 2 squared over 2 to the power of 4 minus 3 over 5 end cell row blank equals cell 2 to the power of negative 2 end exponent minus 3 over 5 end cell row blank equals cell 1 over 2 squared minus 3 over 5 end cell row blank equals cell 1 fourth minus 3 over 5 end cell row blank equals cell fraction numerator 5 times 1 minus 4 times 3 over denominator 4 times 5 end fraction end cell row blank equals cell fraction numerator 5 minus 12 over denominator 20 end fraction end cell row blank equals cell negative 7 over 20 end cell row blank equals cell negative 0 comma 35 end cell end table    

Dengan demikian, hasil dari open parentheses 2 over 3 close parentheses squared times open parentheses negative 3 over 4 close parentheses squared minus 3 over 2 cubed colon 5 over 8  adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 0 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank comma end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 35 end table

Jadi, jawaban yang tepat adalah D

0

Roboguru

Sederhanakanlah: b.

Pembahasan Soal:

Ingat kembali:

a to the power of m over a to the power of n equals a to the power of m minus n end exponent comma space a not equal to 0 

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

a over b colon c over d equals a over b cross times d over c

sehingga diperoleh perhitungan:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator x squared times y squared over denominator z cubed end fraction colon fraction numerator x cubed times y over denominator z squared end fraction end cell equals cell fraction numerator x squared times y squared over denominator z cubed end fraction cross times fraction numerator z squared over denominator x cubed times y end fraction end cell row blank equals cell fraction numerator x squared times y squared times z squared over denominator x cubed times y times z cubed end fraction end cell row blank equals cell x to the power of 2 minus 3 end exponent times y to the power of 2 minus 1 end exponent times z to the power of 2 minus 3 end exponent end cell row blank equals cell x to the power of negative 1 end exponent times y to the power of 1 times z to the power of negative 1 end exponent end cell row blank equals cell fraction numerator y over denominator x times z end fraction end cell end table  

Jadi, hasil dari fraction numerator x squared times y squared over denominator z cubed end fraction colon fraction numerator x cubed times y over denominator z squared end fraction adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator y over denominator x times z end fraction end cell end table.

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Roboguru

Nilai  untuk , , dan  adalah ...

Pembahasan Soal:

Sifat-sifat bilangan berpangkat di antaranya sebagai berikut.

a to the power of m over a to the power of n equals a to the power of m minus n end exponenta not equal to 0

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

Penyelesaian soal di atas adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator a squared b cubed c to the power of negative 1 end exponent over denominator a to the power of negative 2 end exponent b c squared end fraction end cell equals cell a to the power of 2 minus open parentheses negative 2 close parentheses end exponent times b to the power of 3 minus 1 end exponent times c to the power of negative 1 minus 2 end exponent end cell row blank equals cell a to the power of 4 times b squared times c to the power of negative 3 end exponent end cell row blank equals cell fraction numerator a to the power of 4 times b squared over denominator c cubed end fraction end cell row blank equals cell fraction numerator 2 to the power of 4 times 3 squared over denominator 5 cubed end fraction end cell row blank equals cell fraction numerator 16 times 9 over denominator 125 end fraction end cell row blank equals cell 144 over 125 end cell end table

Oleh karena itu, jawaban yang tepat adalah B.

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