Pertanyaan

Tentukan hasil operasi bilanganberikut dalam bentuk akar! d. ( 4 a × 3 4 a 3 ) 3 e. ( 4 3 6 x ÷ 3 12 x ) 3 f. ( 3 8 b 2 × 3 b 3 ) 4

Tentukan hasil operasi bilangan berikut dalam bentuk akar!
d. $(4 a \times 3 4 a^{3})^{3}$
e. $(4 3 6 x \div 3 12 x)^{3}$
f. $(3 8 b^{2} \times 3 b^{3})^{4}$

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

d. Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu maka diperoleh sebagai berikut. Berdasarkan sifat bilangan berpangkat yaitu maka Berdasarkan sifat bilangan berpangkat maka Berdasarkan sifat bilangan berpangkat maka Berdasarkan sifat bilangan berpangkat pecahan yaitu maka Berdasarkan aturan perkalian bentuk akar dengan akar pangkat sama yaitu maka Jadi hasil dari dalam bentuk akar adalah . e. Berdasarkan aturan pembagian bentuk akar dengan akar pangkat sama yaitu maka diperoleh sebagai berikut. Berdasarkan sifat bilangan berpangkat yaitu maka Ingat bahwa maka Jadi hasil dari adalah . f.Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu maka diperoleh sebagai berikut. Berdasarkan sifat bilangan berpangkat yaitu maka Berdasarkan sifat bilangan berpangkat maka Berdasarkan bilangan berpangkat maka Berdasarkan sifat bilangan berpangkat pecahan yaitu maka Jadi hasil dari adalah

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

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

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

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

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.

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

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 .

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

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

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

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

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