Roboguru

22.23.24=...

Pertanyaan

2 squared.2 cubed.2 to the power of 4 equals...  

  1. 2 to the power of 9 

  2. 2 to the power of 24 

  3. 8 to the power of 9 

  4. 8 to the power of 10 

  5. 8 to the power of 24 

Pembahasan Soal:

Ingat!

Sifat bilangan berpangkat:

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 

Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 squared.2 cubed.2 to the power of 4 end cell equals cell 2 to the power of 2 plus 3 end exponent.2 to the power of 4 end cell row blank equals cell 2 to the power of 5.2 to the power of 4 end cell row blank equals cell 2 to the power of 5 plus 4 end exponent end cell row blank equals cell 2 to the power of 9 end cell end table 


Jadi, jawaban yang tepat adalah A.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. Hajrianti

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Terakhir diupdate 06 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Penyelesaian pertidaksamaan 4⋅2x2+1>(21​)5x+1 adalah ...

Pembahasan Soal:

Diketahui:

Pertidaksamaan 4 times 2 to the power of x squared plus 1 end exponent greater than open parentheses 1 half close parentheses to the power of 5 x plus 1 end exponent

Ditanya:

Pernyelesaian pertidaksamaan tersebut.

Jika terdapat suatu pertidaksamaan dimana a greater than 1 dan a to the power of f open parentheses x close parentheses end exponent greater than a to the power of g left parenthesis x right parenthesis end exponent maka f open parentheses x close parentheses greater than g open parentheses x close parentheses.

Perlu diingat bahwa:

1 over k to the power of l equals k to the power of negative l end exponent k to the power of open parentheses l plus m close parentheses end exponent equals k to the power of l times k to the power of m open parentheses k to the power of l close parentheses to the power of m equals k to the power of l times m end exponent 

Perhatikan perhitungan berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 times 2 to the power of x squared plus 1 end exponent end cell greater than cell open parentheses 1 half close parentheses to the power of 5 x plus 1 end exponent end cell row cell 2 squared times 2 to the power of x squared plus 1 end exponent end cell greater than cell open parentheses 2 to the power of negative 1 end exponent close parentheses to the power of 5 x plus 1 end exponent end cell row cell 2 to the power of x squared plus 1 plus 2 end exponent end cell greater than cell 2 to the power of negative 5 x minus 1 end exponent end cell row cell 2 to the power of x squared plus 3 end exponent end cell greater than cell 2 to the power of negative 5 x minus 1 end exponent end cell row cell x squared plus 3 end cell greater than cell negative 5 x minus 1 end cell row cell x squared plus 3 plus 5 x plus 1 end cell greater than cell negative 5 x plus 5 x minus 1 plus 1 end cell row cell x squared plus 5 x plus 4 end cell greater than 0 row cell open parentheses x plus 1 close parentheses open parentheses x plus 4 close parentheses end cell greater than 0 end table
table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 1 end cell equals 0 row x equals cell negative 1 end cell end table atau  table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 4 end cell equals 0 row x equals cell negative 4 end cell end table        

Dengan menggunakan garis bilangan dan melakukan uji titik pada interval, diperoleh solusi dari x squared plus 5 x plus 4 greater than 0 adalah

Oleh sebab itu, didapat himpunan penyelesaiannya adalah open curly brackets x space left enclose space x less than negative 4 end enclose space atau space x greater than negative 1 close curly brackets.

Sehingga, penyelesaian pertidaksamaan 4 times 2 to the power of x squared plus 1 end exponent greater than open parentheses 1 half close parentheses to the power of 5 x plus 1 end exponent adalah x less than negative 4 space atau space x greater than negative 1.

Jadi, jawaban yang tepat adalah B.

3

Roboguru

3625​=...

Pembahasan Soal:

Ingat bahwa:

  • n-th root of a to the power of m end root equals a to the power of m over n end exponent comma thin space    thin space a greater or equal than 0 
  • a to the power of m over n end exponent equals open parentheses a to the power of m close parentheses to the power of 1 over n end exponent equals n-th root of a to the power of m end root a to the power of m over n end exponent equals open parentheses a to the power of 1 over n end exponent close parentheses to the power of m equals open parentheses n-th root of a close parentheses to the power of m 

Mencari hasil dari akar tersebut:

table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of 625 end cell equals cell cube root of 5 to the power of 4 end root end cell row blank equals cell 5 to the power of 4 over 3 end exponent end cell row blank equals cell 5 to the power of 1 1 third end exponent end cell row blank equals cell 5 to the power of 1 plus 1 third end exponent end cell row blank equals cell 5 to the power of 1 cross times 5 to the power of 1 third end exponent end cell row blank equals cell 5 cross times cube root of 5 to the power of 1 end root end cell row blank equals cell 5 cube root of 5 end cell end table 

Jadi, hasil dari cube root of 625 equals 5 cube root of 5.

Dengan demikian, jawaban yang tepat adalah C.

0

Roboguru

392​⋅3332​=...

Pembahasan Soal:

Ingat bahwa:

  • n-th root of a to the power of m end root equals a to the power of m over n end exponent comma thin space    thin space a greater or equal than 0 
  • a to the power of m over n end exponent equals open parentheses a to the power of m close parentheses to the power of 1 over n end exponent equals n-th root of a to the power of m end root a to the power of m over n end exponent equals open parentheses a to the power of 1 over n end exponent close parentheses to the power of m equals open parentheses n-th root of a close parentheses to the power of m 
  • a to the power of m times a to the power of n equals a to the power of m plus n end exponent 

Mencari hasil dari akar tersebut:

3923332=========33923233322323334323334+2333633363323927  

Jadi, hasil dari cube root of 9 squared end root times 3 cube root of 3 squared end root equals 27.

Dengan demikian, jawaban yang tepat adalah B.

0

Roboguru

1632​⋅1631​=...

Pembahasan Soal:

Ingat bahwa:

a to the power of m times a to the power of n equals a to the power of m plus n end exponent 

Mencari hasil dari akar tersebut:

table attributes columnalign right center left columnspacing 0px end attributes row cell 16 to the power of 2 over 3 end exponent times 16 to the power of 1 third end exponent end cell equals cell 16 to the power of 2 over 3 plus 1 third end exponent end cell row blank equals cell 16 to the power of 1 end cell row blank equals 16 end table 

Jadi, hasil dari 16 to the power of 2 over 3 end exponent times 16 to the power of 1 third end exponent equals 16.

Dengan demikian, jawaban yang tepat adalah E.

0

Roboguru

42⋅7243⋅(3,5)2​=...

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 fraction numerator 4 cubed times open parentheses 3 comma 5 close parentheses squared over denominator 4 squared times 7 squared end fraction end cell equals cell fraction numerator 4 cubed times open parentheses begin display style 35 over 10 end style close parentheses squared over denominator 4 squared times 7 squared end fraction end cell row blank equals cell fraction numerator open parentheses 2 squared close parentheses cubed times open parentheses begin display style 7 over 2 end style close parentheses squared over denominator open parentheses 2 squared close parentheses squared times 7 squared end fraction end cell row blank equals cell fraction numerator 2 to the power of 2 times 3 end exponent times begin display style 7 squared over 2 squared end style over denominator 2 to the power of 2 times 2 end exponent times 7 squared end fraction end cell row blank equals cell fraction numerator 2 to the power of 6 times begin display style 7 squared over 2 squared end style over denominator 2 to the power of 4 times 7 squared end fraction end cell row blank equals cell fraction numerator 2 to the power of 6 times 7 squared times 2 to the power of negative 1 end exponent over denominator 2 to the power of 4 times 7 squared end fraction end cell row blank equals cell 2 to the power of 6 plus open parentheses negative 1 close parentheses minus 4 end exponent times 7 to the power of 2 minus 2 end exponent end cell row blank equals cell 2 to the power of 1 times 7 to the power of 0 end cell row blank equals cell 2 times 1 end cell row blank equals 2 end table

Dengan demikian, hasil dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 4 cubed times open parentheses 3 comma 5 close parentheses squared over denominator 4 squared times 7 squared end fraction end cell end table  adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table

Jadi, jawaban yang tepat adalah D

2

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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