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Sederhanakan l. 2(5p2)3=...

Pertanyaan

Sederhanakan

l. 2(5p2)3=...

Pembahasan Soal:

Ingat!

Sifat bilangan berangkat:

  • (a×b)n=an×bn 
  • (am)n=am×n   

Sehingga:

2(5p2)3====2×53×p2×32×125×p6250×p6250p6 

Dengan demikian, bentuk sederhana dari 2(5p2)3 adalah 250p6.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Sutiawan

Mahasiswa/Alumni Universitas Pasundan

Terakhir diupdate 30 Agustus 2021

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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

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

Nilai dari:   adalah ....

Pembahasan Soal:

Perhatikan bentuk selisih dua kuadrat berikut!

open parentheses a plus b close parentheses open parentheses a minus b close parentheses equals a squared minus b squared 

Dengan menerapkan rumus di atas, diperoleh perhitungan sebagai berikut.

begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis a to the power of 1 over 8 end exponent plus a to the power of negative 1 over 8 end exponent right parenthesis left parenthesis a to the power of 1 over 8 end exponent minus a to the power of negative 1 over 8 end exponent right parenthesis left parenthesis a to the power of 1 fourth end exponent plus a to the power of negative 1 fourth end exponent right parenthesis left parenthesis a to the power of 1 half end exponent plus a to the power of negative 1 half end exponent right parenthesis end cell row blank equals cell open square brackets open parentheses a to the power of 1 over 8 end exponent close parentheses squared minus open parentheses a to the power of negative 1 over 8 end exponent close parentheses squared close square brackets left parenthesis a to the power of 1 fourth end exponent plus a to the power of negative 1 fourth end exponent right parenthesis left parenthesis a to the power of 1 half end exponent plus a to the power of negative 1 half end exponent right parenthesis end cell row blank equals cell left parenthesis a to the power of 1 fourth end exponent minus a to the power of negative 1 fourth end exponent right parenthesis left parenthesis a to the power of 1 fourth end exponent plus a to the power of negative 1 fourth end exponent right parenthesis left parenthesis a to the power of 1 half end exponent plus a to the power of negative 1 half end exponent right parenthesis end cell row blank equals cell open square brackets open parentheses a to the power of 1 fourth end exponent close parentheses squared minus open parentheses a to the power of negative 1 fourth end exponent close parentheses squared close square brackets left parenthesis a to the power of 1 half end exponent plus a to the power of negative 1 half end exponent right parenthesis end cell row blank equals cell left parenthesis a to the power of 1 half end exponent minus a to the power of negative 1 half end exponent right parenthesis left parenthesis a to the power of 1 half end exponent plus a to the power of negative 1 half end exponent right parenthesis end cell row blank equals cell open square brackets open parentheses a to the power of 1 half end exponent close parentheses squared minus open parentheses a to the power of negative 1 half end exponent close parentheses squared close square brackets end cell row blank equals cell a minus a to the power of negative 1 end exponent end cell end table end style 

Jadi, nilai dari begin mathsize 12px style open parentheses a to the power of 1 over 8 end exponent plus a to the power of negative 1 over 8 end exponent close parentheses open parentheses a to the power of 1 over 8 end exponent minus a to the power of negative 1 over 8 end exponent close parentheses open parentheses a to the power of 1 fourth end exponent plus a to the power of negative 1 fourth end exponent close parentheses open parentheses a to the power of 1 half end exponent plus a to the power of negative 1 half end exponent close parentheses end style adalah a minus a to the power of negative 1 end exponent.

Dengan demikian, jawaban yang tepat adalah B.

0

Roboguru

Bentuk sederhana dari  adalah ....

Pembahasan Soal:

open parentheses fraction numerator 4 a squared b cubed over denominator 6 a b to the power of 5 end fraction close parentheses to the power of negative 1 end exponent space equals space fraction numerator 6 a b to the power of 5 over denominator 4 a squared b cubed end fraction space equals space fraction numerator 3 b to the power of 5 minus 2 end exponent over denominator 2 a to the power of 2 minus 1 end exponent end fraction space equals space fraction numerator 3 b squared over denominator 2 a end fraction

1

Roboguru

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

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

Penyelesaian soal di atas, yaitu

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator open parentheses 4 a squared b cubed close parentheses to the power of 5 over denominator 2 to the power of 7 a to the power of 9 b to the power of 6 end fraction end cell equals cell fraction numerator open parentheses 2 squared close parentheses to the power of 5 open parentheses a squared close parentheses to the power of 5 open parentheses b cubed close parentheses to the power of 5 over denominator 2 to the power of 7 a to the power of 9 b to the power of 6 end fraction end cell row blank equals cell fraction numerator 2 to the power of 10 a to the power of 10 b to the power of 15 over denominator 2 to the power of 7 a to the power of 9 b to the power of 6 end fraction end cell row blank equals cell 2 to the power of 10 minus 7 end exponent a to the power of 10 minus 9 end exponent b to the power of 15 minus 6 end exponent end cell row blank equals cell 2 cubed a b to the power of 9 end cell end table

Dengan demikian, bentuk sederhana dari table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator open parentheses 4 a squared b cubed close parentheses to the power of 5 over denominator 2 to the power of 7 a to the power of 9 b to the power of 6 end fraction end cell equals cell 2 cubed a b to the power of 9 end cell end table

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Roboguru

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