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Pertanyaan

Hasil dari cube root of a squared end root cross times a fourth root of a cubed end root adalah ....

  1. 2 a root index 12 of a to the power of 5 end root

  2. a squared space root index 12 of a to the power of 5 end root

  3. 2 a space root index 12 of a to the power of 10 end root

  4. a squared space root index 12 of a to the power of 10 end root

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Diketahui cube root of a squared end root cross times a fourth root of a cubed end root memiliki akar pangkat yang berbeda sehingga untuk menentukan hasil perkaliannya maka diperlukan merebah bentuk akar menjadi bilangan berpangkat.

Jika a not equal to 0 space text dan end text space n comma m bilangan positif maka berlaku:

n-th root of a to the power of m end root equals a to the power of m over n end exponent

Maka

cube root of a squared end root cross times a fourth root of a cubed end root equals a to the power of 2 over 3 end exponent cross times a open parentheses a to the power of 3 over 4 end exponent close parentheses

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 dan a to the power of 1 equals a maka diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of a squared end root cross times a fourth root of a cubed end root end cell equals cell a to the power of 2 over 3 end exponent cross times a open parentheses a to the power of 3 over 4 end exponent close parentheses end cell row blank equals cell a to the power of 2 over 3 end exponent cross times a cross times a to the power of 3 over 4 end exponent end cell row blank equals cell a cross times a to the power of 2 over 3 plus 3 over 4 end exponent end cell row blank equals cell a cross times a to the power of fraction numerator 2 cross times 4 over denominator 12 end fraction plus fraction numerator 3 cross times 3 over denominator 12 end fraction end exponent end cell row blank equals cell a cross times a to the power of 8 over 12 plus 9 over 12 end exponent end cell row blank equals cell a cross times a to the power of 17 over 12 end exponent end cell row blank equals cell a cross times a to the power of 12 over 12 plus 5 over 12 end exponent end cell row blank equals cell a cross times a to the power of 12 over 12 end exponent cross times a to the power of 5 over 12 end exponent end cell row blank equals cell a cross times a to the power of 1 cross times a to the power of 5 over 12 end exponent end cell row blank equals cell a cross times a cross times a to the power of 5 over 12 end exponent end cell row blank equals cell a squared cross times a to the power of 5 over 12 end exponent end cell end table

Berdasarkan sifat bilangan berpangkat pecahan 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 cube root of a squared end root cross times a fourth root of a cubed end root end cell equals cell a squared cross times a to the power of 5 over 12 end exponent end cell row blank equals cell a squared cross times root index 12 of a to the power of 5 end root end cell row blank equals cell a squared space root index 12 of a to the power of 5 end root end cell end table

Jadi hasil dari cube root of a squared end root cross times a fourth root of a cubed end root adalah a squared space root index 12 of a to the power of 5 end root.

Oleh karena itu, jawaban yang benar adalah B.

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