Roboguru

Sederhanakan n. 8pq2r2(4p2qr5)3​=...

Pertanyaan

Sederhanakan

n. 8pq2r2(4p2qr5)3=...

Pembahasan Soal:

Ingat!

Sifat bilangan berangkat:

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

Sehingga:

8pq2r2(4p2qr5)3=====8pq2r243(p2)3q3(r5)38pq2r264p2×3q3r5×38pq2r264p6q3r158p61q32r1528p5qr13 

Dengan demikian, bentuk sederhana dari 8pq2r2(4p2qr5)3 adalah 8p5qr13.

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

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

Gunakan sifat-sifat operasi bilangan berpangkat untuk menyederhanakan operasi aljabar berikut. d.

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

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

Penyelesaian soal di atas, yaitu

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 squared p cubed q to the power of 4 close parentheses cubed over open parentheses 3 p squared q cubed close parentheses to the power of 4 end cell equals cell fraction numerator open parentheses 3 squared close parentheses cubed open parentheses p cubed close parentheses cubed open parentheses q to the power of 4 close parentheses cubed over denominator 3 to the power of 4 open parentheses p squared close parentheses to the power of 4 open parentheses q cubed close parentheses to the power of 4 end fraction end cell row blank equals cell fraction numerator 3 to the power of 6 p to the power of 9 q to the power of 12 over denominator 3 to the power of 4 p to the power of 8 q to the power of 12 end fraction end cell row blank equals cell 3 to the power of 6 minus 4 end exponent p to the power of 9 minus 8 end exponent q to the power of 12 minus 12 end exponent end cell row blank equals cell 3 squared p q to the power of 0 end cell row blank equals cell 3 squared p times 1 end cell row blank equals cell 9 p end cell end table

Dengan demikian, bentuk sederhana dari table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 squared p cubed q to the power of 4 close parentheses cubed over open parentheses 3 p squared q cubed close parentheses to the power of 4 end cell equals cell 9 p end cell end table 

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. 

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Roboguru

Bentuk sederhana dari  adalah ...

Pembahasan Soal:

Ingat bahwa:

  • open parentheses a to the power of n close parentheses to the power of m equals a to the power of n cross times m end exponent 
  • a to the power of n a to the power of m equals a to the power of n plus 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 

Menyederhanakan bentuk open parentheses a to the power of negative 4 end exponent times b cubed times c cubed close parentheses cubed over open parentheses a to the power of negative 2 end exponent times b to the power of 4 times c cubed close parentheses to the power of negative 2 end exponent:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a to the power of negative 4 end exponent times b cubed times c cubed close parentheses cubed over open parentheses a to the power of negative 2 end exponent times b to the power of 4 times c cubed close parentheses to the power of negative 2 end exponent end cell equals cell fraction numerator a to the power of negative 4 cross times 3 end exponent times b to the power of 3 cross times 3 end exponent times c to the power of 3 cross times 3 end exponent over denominator a to the power of negative 2 cross times negative 2 end exponent times b to the power of 4 cross times negative 2 end exponent times c to the power of 3 cross times negative 2 end exponent end fraction end cell row blank equals cell fraction numerator a to the power of negative 12 end exponent b to the power of 9 c to the power of 9 over denominator a to the power of 4 b to the power of negative 8 end exponent c to the power of negative 6 end exponent end fraction end cell row blank equals cell a to the power of negative 12 plus left parenthesis negative 4 right parenthesis end exponent b to the power of 9 minus left parenthesis negative 8 right parenthesis end exponent c to the power of 9 minus left parenthesis negative 6 right parenthesis end exponent end cell row blank equals cell a to the power of negative 16 end exponent b to the power of 17 c to the power of 15 end cell end table 

Jadi, bentuk sederhana dari open parentheses a to the power of negative 4 end exponent times b cubed times c cubed close parentheses cubed over open parentheses a to the power of negative 2 end exponent times b to the power of 4 times c cubed close parentheses to the power of negative 2 end exponent adalah a to the power of negative 16 end exponent b to the power of 17 c to the power of 15.

0

Roboguru

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

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

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 x to the power of negative 4 end exponent y cubed over denominator x to the power of negative 2 end exponent y squared end fraction close parentheses to the power of negative 5 end exponent end cell equals cell open parentheses x to the power of negative 4 minus open parentheses negative 2 close parentheses end exponent y to the power of 3 minus 2 end exponent close parentheses to the power of negative 5 end exponent end cell row blank equals cell open parentheses x to the power of negative 2 end exponent y close parentheses to the power of negative 5 end exponent end cell row blank equals cell open parentheses x to the power of negative 2 end exponent close parentheses to the power of negative 5 end exponent open parentheses y close parentheses to the power of negative 5 end exponent end cell row blank equals cell x to the power of 10 y to the power of negative 5 end exponent end cell row blank equals cell x to the power of 10 over y to the power of 5 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 x to the power of negative 4 end exponent y cubed over denominator x to the power of negative 2 end exponent y squared end fraction close parentheses to the power of negative 5 end exponent end cell equals cell x to the power of 10 over y to the power of 5 end cell end table 

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Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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