Roboguru

Tentukan hasil operasi bilangan berikut dalam bentuk akar! d. (4a​×34a3​)3 e. (436x​÷312x​)3 f. (38b2​×3b3​)4

Pertanyaan

Tentukan hasil operasi bilangan berikut dalam bentuk akar!
d. open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed
e. open parentheses 4 cube root of 6 x end root divided by cube root of 12 x end root close parentheses cubed
f. open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4

Pembahasan Soal:

d. Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu n-th root of a to the power of m end root equals a to the power of m over n end exponent comma a not equal to 0 maka open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed diperoleh sebagai berikut.

open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed equals open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent cross times 3 a to the power of 3 over 4 end exponent close parentheses cubed

Berdasarkan sifat bilangan berpangkat yaitu 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 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed end cell equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent cross times 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell row blank equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent close parentheses cubed cross times open parentheses 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell end table

Berdasarkan sifat bilangan berpangkat 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 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed end cell equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent cross times 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell row blank equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent close parentheses cubed cross times open parentheses 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell row blank equals cell open parentheses 4 a close parentheses to the power of 1 half cross times 3 end exponent cross times open parentheses 3 a close parentheses to the power of 3 over 4 cross times 3 end exponent end cell row blank equals cell open parentheses 4 a close parentheses to the power of 3 over 2 end exponent cross times open parentheses 3 a close parentheses to the power of 9 over 4 end exponent end cell end table

Berdasarkan 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 open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed end cell equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent cross times 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell row blank equals cell open parentheses open parentheses 4 a close parentheses to the power of 1 half end exponent close parentheses cubed cross times open parentheses 3 a to the power of 3 over 4 end exponent close parentheses cubed end cell row blank equals cell open parentheses 4 a close parentheses to the power of 1 half cross times 3 end exponent cross times open parentheses 3 a close parentheses to the power of 3 over 4 cross times 3 end exponent end cell row blank equals cell open parentheses 4 a close parentheses to the power of 3 over 2 end exponent cross times open parentheses 3 a close parentheses to the power of 9 over 4 end exponent end cell row blank equals cell 4 to the power of 3 over 2 end exponent cross times a to the power of 3 over 2 end exponent cross times 3 to the power of 9 over 4 end exponent cross times a to the power of 9 over 4 end exponent end cell row blank equals cell open parentheses 2 squared close parentheses to the power of 3 over 2 end exponent cross times a to the power of 3 over 2 plus 9 over 4 end exponent cross times 3 to the power of fraction numerator 8 plus 1 over denominator 4 end fraction end exponent end cell row blank equals cell 2 to the power of 2 cross times 3 over 2 end exponent cross times a to the power of fraction numerator 3 cross times 2 plus 9 over denominator 4 end fraction end exponent cross times 3 to the power of 8 over 4 plus 1 fourth end exponent end cell row blank equals cell 2 cubed cross times a to the power of fraction numerator 6 plus 9 over denominator 4 end fraction end exponent cross times 3 to the power of 2 plus 1 fourth end exponent end cell row blank equals cell 8 cross times a to the power of 15 over 4 end exponent cross times 3 squared cross times 3 to the power of 1 fourth end exponent end cell row blank equals cell 8 cross times 9 cross times a to the power of fraction numerator 12 plus 3 over denominator 4 end fraction end exponent cross times 3 to the power of 1 fourth end exponent end cell row blank equals cell 72 cross times a to the power of 12 over 4 plus 3 over 4 end exponent cross times 3 to the power of 1 fourth end exponent end cell row blank equals cell 72 cross times a cubed cross times a to the power of 3 over 4 end exponent cross times 3 to the power of 1 fourth end exponent end cell row blank blank blank end table

Berdasarkan sifat bilangan berpangkat pecahan yaitu a to the power of m over n end exponent equals n-th root of a to the power of m end root comma space a not equal to 0 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed end cell equals cell 72 cross times a cubed cross times a to the power of 3 over 4 end exponent cross times 3 to the power of 1 fourth end exponent end cell row blank equals cell 72 cross times a cubed cross times fourth root of a cubed end root cross times fourth root of 3 to the power of 1 end root end cell row blank equals cell 72 a cubed cross times fourth root of a cubed end root cross times fourth root of 3 end cell row blank blank blank end table

Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu n-th root of a cross times n-th root of b equals n-th root of a cross times b end root maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed end cell equals cell 72 cross times a cubed cross times a to the power of 3 over 4 end exponent cross times 3 to the power of 1 fourth end exponent end cell row blank equals cell 72 cross times a cubed cross times fourth root of a cubed end root cross times fourth root of 3 to the power of 1 end root end cell row blank equals cell 72 a cubed cross times fourth root of a cubed end root cross times fourth root of 3 end cell row blank equals cell 72 a cubed cross times fourth root of a cubed cross times 3 end root end cell row blank equals cell 72 a cubed fourth root of 3 a cubed end root end cell row blank blank blank end table

Jadi hasil dari open parentheses square root of 4 a end root cross times 3 fourth root of a cubed end root close parentheses cubed dalam bentuk akar adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 72 a cubed fourth root of 3 a cubed end root end cell row blank blank blank end table.

e. Berdasarkan aturan pembagian bentuk akar dengan akar pangkat sama yaitu fraction numerator n-th root of a over denominator n-th root of b end fraction equals n-th root of a over b end root maka open parentheses 4 cube root of 6 x end root divided by cube root of 12 x end root close parentheses cubed diperoleh sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 4 cube root of 6 x end root divided by cube root of 12 x end root close parentheses cubed end cell equals cell open parentheses fraction numerator 4 cube root of 6 x end root over denominator cube root of 12 x end root end fraction close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of fraction numerator 6 x over denominator 12 x end fraction end root close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of 1 half end root close parentheses cubed end cell end table

Berdasarkan sifat bilangan berpangkat yaitu 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 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 4 cube root of 6 x end root divided by cube root of 12 x end root close parentheses cubed end cell equals cell open parentheses fraction numerator 4 cube root of 6 x end root over denominator cube root of 12 x end root end fraction close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of fraction numerator 6 x over denominator 12 x end fraction end root close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of 1 half end root close parentheses cubed end cell row blank equals cell 4 cubed cross times open parentheses cube root of 1 half end root close parentheses cubed end cell end table

Ingat bahwa n-th root of a to the power of m end root equals open parentheses n-th root of a close parentheses to the power of m maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 4 cube root of 6 x end root divided by cube root of 12 x end root close parentheses cubed end cell equals cell open parentheses fraction numerator 4 cube root of 6 x end root over denominator cube root of 12 x end root end fraction close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of fraction numerator 6 x over denominator 12 x end fraction end root close parentheses cubed end cell row blank equals cell open parentheses 4 cross times cube root of 1 half end root close parentheses cubed end cell row blank equals cell 4 cubed cross times open parentheses cube root of 1 half end root close parentheses cubed end cell row blank equals cell 64 cross times cube root of open parentheses 1 half close parentheses cubed end root end cell row blank equals cell 64 cross times 1 half end cell row blank equals 32 end table

Jadi hasil dari open parentheses 4 cube root of 6 x end root divided by cube root of 12 x end root close parentheses cubed adalah 32.

f. Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu n-th root of a to the power of m end root equals a to the power of m over n end exponent comma a not equal to 0 maka open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 diperoleh sebagai berikut.

open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 equals open parentheses open parentheses 8 b squared close parentheses to the power of 1 third end exponent cross times 3 cross times b to the power of 3 over 2 end exponent close parentheses to the power of 4

Berdasarkan sifat bilangan berpangkat yaitu 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 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 end cell equals cell open parentheses open parentheses 8 b squared close parentheses to the power of 1 third end exponent cross times 3 cross times b to the power of 3 over 2 end exponent close parentheses to the power of 4 end cell row blank equals cell open parentheses open parentheses 8 b squared close parentheses to the power of 1 third end exponent close parentheses to the power of 4 cross times 3 to the power of 4 cross times open parentheses b to the power of 3 over 2 end exponent close parentheses to the power of 4 end cell end table

Berdasarkan sifat bilangan berpangkat 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 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 end cell equals cell open parentheses open parentheses 8 b squared close parentheses to the power of 1 third end exponent cross times 3 cross times b to the power of 3 over 2 end exponent close parentheses to the power of 4 end cell row blank equals cell open parentheses open parentheses 8 b squared close parentheses to the power of 1 third end exponent close parentheses to the power of 4 cross times 3 to the power of 4 cross times open parentheses b to the power of 3 over 2 end exponent close parentheses to the power of 4 end cell row blank equals cell open parentheses 8 b squared close parentheses to the power of 1 third cross times 4 end exponent cross times 81 cross times b to the power of 3 over 2 cross times 4 end exponent end cell row blank equals cell open parentheses 8 b squared close parentheses to the power of 3 over 4 end exponent cross times 81 cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 2 cross times 3 over 4 end exponent cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 3 over 2 end exponent cross times b to the power of 6 end cell end table

Berdasarkan 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 open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 end cell equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 3 over 2 end exponent cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of fraction numerator 2 plus 1 over denominator 2 end fraction end exponent cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 2 over 2 plus 1 half end exponent cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 1 cross times b to the power of 1 half end exponent cross times b to the power of 6 end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 1 plus 6 end exponent cross times b to the power of 1 half end exponent end cell row blank equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 7 cross times b to the power of 1 half end exponent end cell end table

Berdasarkan sifat bilangan berpangkat pecahan yaitu a to the power of m over n end exponent equals n-th root of a to the power of m end root maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 end cell equals cell 81 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 7 cross times b to the power of 1 half end exponent end cell row blank equals cell 81 b to the power of 7 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of fraction numerator 1 cross times 2 over denominator 2 cross times 2 end fraction end exponent end cell row blank equals cell 81 b to the power of 7 cross times 8 to the power of 3 over 4 end exponent cross times b to the power of 2 over 4 end exponent end cell row blank equals cell 81 b to the power of 7 fourth root of 8 cubed b squared end root end cell end table

Jadi hasil dari open parentheses cube root of 8 b squared end root cross times 3 square root of b cubed end root close parentheses to the power of 4 adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 81 b to the power of 7 fourth root of 8 cubed b squared end root. end cell end table

 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. Febrianti

Mahasiswa/Alumni Universitas Negeri Malang

Terakhir diupdate 07 Oktober 2021

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