Roboguru

Bentuksederhanadari3−3a3b−627−1a3b6​=...

Pertanyaan

Bentuk space sederhana space dari space space fraction numerator 27 to the power of negative 1 end exponent space a cubed b to the power of 6 over denominator space 3 to the power of negative 3 end exponent space a cubed b to the power of negative 6 end exponent end fraction space equals...

  1. long dash 3 a cubed b to the power of 6 space end exponent

  2. long dash 3 a to the power of 6 b to the power of 6 space

  3. a to the power of 6 b to the power of 12 space end exponent

  4. 3 a b to the power of 2 space end exponent

  5. b to the power of 12 space

Pembahasan Soal:

Gunakan space sifat minus sifat space perpangkatan space berikut space colon  left parenthesis a to the power of p right parenthesis to the power of q equals a to the power of p q end exponent  a to the power of p over a to the power of q equals a to the power of p minus q end exponent  a to the power of negative p end exponent equals 1 over a to the power of p    S e d e r h a n a k a n space b e n t u k space p a n g k a t space h i n g g a space y a n g space p a l i n g space s e d e r h a n a space  fraction numerator 27 to the power of negative 1 end exponent a cubed b to the power of 6 over denominator 3 to the power of negative 3 end exponent a cubed b to the power of negative 6 end exponent end fraction equals fraction numerator left parenthesis 3 cubed right parenthesis to the power of negative 1 end exponent a cubed b to the power of 6 over denominator 3 to the power of negative 3 end exponent a cubed b to the power of negative 6 end exponent end fraction equals fraction numerator horizontal strike 3 to the power of negative 3 end exponent a cubed end strike b to the power of 6 over denominator horizontal strike 3 to the power of negative 3 end exponent a cubed end strike b to the power of negative 6 end exponent end fraction equals b to the power of 12

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Intan

Mahasiswa/Alumni Institut Pertanian Bogor

Terakhir diupdate 04 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Tentukan hasil pemangkatan berikut! d. (−5a−2)−3 e. (2a2b3)−6 f. (3a3b−4)−5

Pembahasan Soal:

Ingatlah sifat-sifat bilangan berpangkat berikut.

left parenthesis straight i right parenthesis space 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 left parenthesis ii right parenthesis space 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 left parenthesis iii right parenthesis space open parentheses a b close parentheses to the power of m equals a to the power of m b to the power of m left parenthesis iv right parenthesis space 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 left parenthesis straight v right parenthesis space a to the power of negative m end exponent equals 1 over a to the power of m left parenthesis vi right parenthesis space open parentheses negative a close parentheses to the power of m equals negative a to the power of m space space untuk space m space bil. ganjil  

Berdasarkan sifat-sifat di atas, maka:

d)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative 5 a to the power of negative 2 end exponent close parentheses to the power of negative 3 end exponent end cell equals cell 1 over open parentheses negative 5 a to the power of negative 2 end exponent close parentheses cubed end cell row blank equals cell 1 over open parentheses negative begin display style 5 over a squared end style close parentheses cubed end cell row blank equals cell fraction numerator 1 over denominator open parentheses negative 5 over a squared close parentheses cross times open parentheses negative 5 over a squared close parentheses cross times open parentheses negative 5 over a squared close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator negative begin display style 125 over a to the power of 2 plus 2 plus 2 end exponent end style end fraction end cell row blank equals cell fraction numerator 1 over denominator negative begin display style 125 over a to the power of 6 end style end fraction end cell row blank equals cell negative a to the power of 6 over 125 end cell end table

e)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 2 a squared b cubed close parentheses to the power of negative 6 end exponent end cell equals cell 1 over open parentheses 2 a squared b cubed close parentheses to the power of 6 end cell row blank equals cell fraction numerator 1 over denominator 2 to the power of 6 cross times open parentheses a squared close parentheses to the power of 6 cross times open parentheses b cubed close parentheses to the power of 6 end fraction end cell row blank equals cell fraction numerator 1 over denominator 64 cross times a to the power of 2 cross times 6 end exponent cross times b to the power of 3 cross times 6 end exponent end fraction end cell row blank equals cell fraction numerator 1 over denominator 64 cross times a to the power of 12 cross times b to the power of 18 end fraction end cell row blank equals cell fraction numerator 1 over denominator 64 a to the power of 12 b to the power of 18 end fraction end cell end table

f)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 a cubed b to the power of negative 4 end exponent close parentheses to the power of negative 5 end exponent end cell equals cell 1 over open parentheses 3 a cubed b to the power of negative 4 end exponent close parentheses to the power of 5 end cell row blank equals cell 1 over open parentheses begin display style fraction numerator 3 a cubed over denominator b to the power of 4 end fraction end style close parentheses to the power of 5 end cell row blank equals cell fraction numerator 1 over denominator begin display style open parentheses 3 a cubed close parentheses to the power of 5 over open parentheses b to the power of 4 close parentheses to the power of 5 end style end fraction end cell row blank equals cell open parentheses b to the power of 4 close parentheses to the power of 5 over open parentheses 3 a cubed close parentheses to the power of 5 end cell row blank equals cell fraction numerator b to the power of 20 over denominator 3 to the power of 5 a to the power of 15 end fraction end cell row blank equals cell fraction numerator b to the power of 20 over denominator 243 a to the power of 15 end fraction end cell end table

Dengan demikian, hasil dari  open parentheses negative 5 a to the power of negative 2 end exponent close parentheses to the power of negative 3 end exponent equals 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 cell a to the power of 6 over 125 end cell end table, open parentheses 2 a squared b cubed close parentheses to the power of negative 6 end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator 64 a to the power of 12 b to the power of 18 end fraction end cell end table, dan open parentheses 3 a cubed b to the power of negative 4 end exponent close parentheses to the power of negative 5 end exponent equals fraction numerator b to the power of 20 over denominator 243 a to the power of 15 end fraction.

0

Roboguru

Hasil dari 845​243​×432​​ adalah ...

Pembahasan Soal:

Ingat!

table attributes columnalign right center left columnspacing 0px end attributes 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 n end exponent end cell row cell a to the power of m cross times a to the power of n end cell equals cell a to the power of m plus n end exponent 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 row cell a to the power of m over n end exponent end cell equals cell n-th root of a to the power of m end root end cell end table  

Hasil dari fraction numerator 2 to the power of begin display style 3 over 4 end style end exponent cross times 4 to the power of begin display style 2 over 3 end style end exponent over denominator 8 to the power of begin display style 5 over 4 end style end exponent end fraction adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 to the power of begin display style 3 over 4 end style end exponent cross times 4 to the power of begin display style 2 over 3 end style end exponent over denominator 8 to the power of begin display style 5 over 4 end style end exponent end fraction end cell equals cell fraction numerator 2 to the power of begin display style 3 over 4 end style end exponent cross times open parentheses 2 squared close parentheses to the power of begin display style 2 over 3 end style end exponent over denominator open parentheses 2 cubed close parentheses to the power of begin display style 5 over 4 end style end exponent end fraction end cell row blank equals cell fraction numerator 2 to the power of begin display style 3 over 4 end style end exponent cross times 2 to the power of begin display style 4 over 3 end style end exponent over denominator 2 to the power of begin display style 15 over 4 end style end exponent end fraction end cell row blank equals cell 2 to the power of 3 over 4 plus 4 over 3 minus 15 over 4 end exponent end cell row blank equals cell 2 to the power of fraction numerator open parentheses 3 times 3 close parentheses plus open parentheses 4 times 4 close parentheses minus open parentheses 15 times 3 close parentheses over denominator 12 end fraction end exponent end cell row blank equals cell 2 to the power of negative 20 over 12 end exponent end cell row blank blank blank end table 

JadiError converting from MathML to accessible text..

0

Roboguru

Jika f(n)=22n+2.6n−4 dan g(n)=12n−1 , n bilangan asli, maka g(n)f(n)​=...

Pembahasan Soal:

fraction numerator f left parenthesis n right parenthesis over denominator g left parenthesis n right parenthesis end fraction equals fraction numerator 2 to the power of 2 n plus 2 end exponent.6 to the power of n minus 4 end exponent over denominator 12 to the power of n minus 1 end exponent end fraction  equals fraction numerator 2 to the power of 2 n plus 2 end exponent.2 to the power of n minus 4 end exponent.3 to the power of n minus 4 end exponent over denominator 2 to the power of 2 n minus 2 end exponent.3 to the power of n minus 1 end exponent end fraction  equals 2 to the power of n 3 to the power of negative 3 end exponent  equals 2 to the power of n over 27

1

Roboguru

Tentukan hasil pemangkatan bilangan berpangkat berikut ! a. (4654​)23​ b. (5649​)−31​ c. (−2834​)−43​

Pembahasan Soal:

Ingatlah sifat-sifat bilangan berpangkat berikut.

left parenthesis straight i right parenthesis space 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 left parenthesis ii right parenthesis space 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 left parenthesis iii right parenthesis space 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 left parenthesis iv right parenthesis space a to the power of negative m end exponent equals 1 over a to the power of m  

Berdasarkan sifat-sifat di atas, maka:

a)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 5 to the power of 4 over 4 to the power of 6 close parentheses to the power of 3 over 2 end exponent end cell equals cell open parentheses 5 to the power of 4 close parentheses to the power of begin display style 3 over 2 end style end exponent over open parentheses 4 to the power of 6 close parentheses to the power of begin display style 3 over 2 end style end exponent end cell row blank equals cell 5 to the power of 4 cross times begin display style 3 over 2 end style end exponent over 4 to the power of 6 cross times begin display style 3 over 2 end style end exponent end cell row blank equals cell 5 to the power of begin display style 12 over 2 end style end exponent over 4 to the power of begin display style 18 over 2 end style end exponent end cell row blank equals cell 5 to the power of 6 over 4 to the power of 9 end cell end table

b)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 4 to the power of 9 over 5 to the power of 6 close parentheses to the power of negative 1 third end exponent end cell equals cell open parentheses 4 to the power of 9 close parentheses to the power of negative begin display style 1 third end style end exponent over open parentheses 5 to the power of 6 close parentheses to the power of negative begin display style 1 third end style end exponent end cell row blank equals cell 4 to the power of 9 cross times open parentheses negative begin display style 1 third end style close parentheses end exponent over 5 to the power of 6 cross times open parentheses negative begin display style 1 third end style close parentheses end exponent end cell row blank equals cell 4 to the power of negative 3 end exponent over 5 to the power of negative 2 end exponent end cell row blank equals cell fraction numerator begin display style 1 over 4 cubed end style over denominator begin display style 1 over 5 squared end style end fraction end cell row blank equals cell 5 squared over 4 cubed end cell row blank equals cell 25 over 64 end cell end table

c)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative 3 to the power of 4 over 2 to the power of 8 close parentheses to the power of negative 3 over 4 end exponent end cell equals cell open parentheses open parentheses negative 1 close parentheses times 3 to the power of 4 over 2 to the power of 8 close parentheses to the power of negative 3 over 4 end exponent end cell row blank equals cell open parentheses negative 1 close parentheses to the power of negative 3 over 4 end exponent times open parentheses 3 to the power of 4 over 2 to the power of 8 close parentheses to the power of negative 3 over 4 end exponent end cell row blank equals cell 1 over open parentheses negative 1 close parentheses to the power of begin display style 3 over 4 end style end exponent times open parentheses 3 to the power of 4 close parentheses to the power of negative begin display style 3 over 4 end style end exponent over open parentheses 2 to the power of 8 close parentheses to the power of negative begin display style 3 over 4 end style end exponent end cell row blank equals cell fraction numerator 3 to the power of up diagonal strike 4 cross times open parentheses negative begin display style fraction numerator 3 over denominator up diagonal strike 4 end fraction end style close parentheses end exponent over denominator open parentheses negative 1 close parentheses to the power of 3 over 4 end exponent times 2 to the power of 8 cross times open parentheses negative begin display style 3 over 4 end style close parentheses end exponent end fraction end cell row blank equals cell fraction numerator 3 to the power of negative 3 end exponent over denominator open parentheses negative 1 close parentheses to the power of 3 over 4 end exponent times 2 to the power of negative begin display style 24 over 4 end style end exponent end fraction end cell row blank equals cell fraction numerator begin display style 1 over 3 cubed end style over denominator open parentheses negative 1 close parentheses to the power of 3 over 4 end exponent times 2 to the power of negative 6 end exponent end fraction end cell row blank equals cell fraction numerator begin display style 1 over 27 end style over denominator open parentheses negative 1 close parentheses to the power of 3 over 4 end exponent over 2 to the power of 6 end fraction end cell row blank equals cell fraction numerator 2 to the power of 6 over denominator 27 times open parentheses negative 1 close parentheses to the power of 3 over 4 end exponent end fraction end cell row blank equals cell fraction numerator 64 over denominator 27 times open parentheses negative 1 close parentheses to the power of 3 over 4 end exponent end fraction end cell end table

Dengan demikian, hasil pemangkatan dari  open parentheses 5 to the power of 4 over 4 to the power of 6 close parentheses to the power of 3 over 2 end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 to the power of 6 over 4 to the power of 9 end cell end table, open parentheses 4 to the power of 9 over 5 to the power of 6 close parentheses to the power of negative 1 third end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 25 over 64 end cell end table, dan open parentheses negative 3 to the power of 4 over 2 to the power of 8 close parentheses to the power of negative 3 over 4 end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 64 over denominator 27 times open parentheses negative 1 close parentheses to the power of 3 over 4 end exponent end fraction end cell end table.

4

Roboguru

Dengan menggunakan tanda "" role="math" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEwAAAASCAYAAADxEzisAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAKIPF7gAAAALVJREFUeNrtk7ENgzAQRW8thJglOyA2SssKE...

Pembahasan Soal:

Kita akan menentukan hubungan 1 over 3 to the power of 100 space... space 1 over 4 to the power of 100 dengan menggunakan pemisalan sebagai berikut :

1 over a to the power of n...1 over left parenthesis a plus 1 right parenthesis to the power of n

kita misalkan a equals 2 space & space n equals 3, maka diperoleh:

table attributes columnalign right center left columnspacing 2px end attributes row cell 1 over 2 cubed end cell cell... end cell cell 1 over left parenthesis 2 plus 1 right parenthesis cubed end cell row cell 1 over 2 cubed end cell cell... end cell cell 1 over 3 cubed end cell row cell 1 over 8 end cell cell... end cell cell 1 over 27 end cell row cell 1 over 8 end cell greater than cell 1 over 27 end cell end table

sedemikian sehingga : 

1 over a to the power of n greater than 1 over left parenthesis a plus 1 right parenthesis to the power of n,

Jika a equals 3 space & space n equals 100, maka diperoleh:

table attributes columnalign right center left columnspacing 2px end attributes row cell 1 over 3 to the power of 100 end cell greater than cell 1 over left parenthesis 3 plus 1 right parenthesis to the power of 100 end cell row cell 1 over 3 to the power of 100 end cell greater than cell 1 over 4 to the power of 100 end cell end table

Jadi, table attributes columnalign right center left columnspacing 2px end attributes row cell 1 over 3 to the power of 100 end cell greater than cell 1 over 4 to the power of 100 end cell end table.

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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