Pertanyaan

Tentukan hasil operasi bilanganberikut dalam bentuk akar! c. ( p 4 3 q − 3 1 r ) 4

Tentukan hasil operasi bilangan berikut dalam bentuk akar!
c. $(p^{\frac{3}{4}} q^{- \frac{1}{3}} r)^{4}$

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R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

hasil operasi bilangan berikut dalam bentuk akar adalah

hasil operasi bilangan open parentheses p to the power of 3 over 4 end exponent q to the power of negative 1 third end exponent square root of r close parentheses to the power of 4

open parentheses p to the power of 3 over 4 end exponent q to the power of negative 1 third end exponent square root of r close parentheses to the power of 4

berikut dalam bentuk akar adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator p cubed r squared over denominator cube root of q to the power of 4 end root end fraction. end cell end table$

Pembahasan

Bentuk akar dapat diubah menjadi bilangan berpangkat yaitu maka diperoleh sebagai berikut. Berdasarkan sifat bilangan berpangkat maka Berdasarkan sifat bilangan berpangkat maka Berdasarkan sifat bilangan berpangkat maka Berdasarkan sifat bilangan berpangkat pecahan yaitu maka Jadihasil operasi bilangan berikut dalam bentuk akar adalah

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 space a not equal to 0 maka open parentheses p to the power of 3 over 4 end exponent q to the power of negative 1 third end exponent square root of r close parentheses to the power of 4 diperoleh sebagai berikut.

open parentheses p to the power of 3 over 4 end exponent q to the power of negative 1 third end exponent square root of r close parentheses to the power of 4 equals open parentheses p to the power of 3 over 4 end exponent q to the power of negative 1 third end exponent r to the power of 1 half end exponent close parentheses to the power of 4

Berdasarkan sifat bilangan berpangkat 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 negative n end exponent equals 1 over a to the power of n comma space a not equal to 0 maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses p to the power of 3 over 4 end exponent q to the power of negative 1 third end exponent square root of r close parentheses to the power of 4 end cell equals cell open parentheses p to the power of 3 over 4 end exponent q to the power of negative 1 third end exponent r to the power of 1 half end exponent close parentheses to the power of 4 end cell row blank equals cell open parentheses p to the power of 3 over 4 end exponent close parentheses to the power of 4 open parentheses q to the power of negative 1 third end exponent close parentheses to the power of 4 open parentheses r to the power of 1 half end exponent close parentheses to the power of 4 end cell row blank equals cell p to the power of 3 over 4 cross times 4 end exponent q to the power of negative 1 third cross times 4 end exponent r to the power of 1 half cross times 4 end exponent end cell row blank equals cell p cubed q to the power of negative 4 over 3 end exponent r squared end cell row blank equals cell p cubed cross times 1 over q to the power of begin display style 4 over 3 end style end exponent cross times r squared end cell row blank equals cell fraction numerator p cubed r squared over denominator q to the power of begin display style 4 over 3 end style end exponent end fraction end cell end table$

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 operasi bilangan open parentheses p to the power of 3 over 4 end exponent q to the power of negative 1 third end exponent square root of r close parentheses to the power of 4 berikut dalam bentuk akar adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator p cubed r squared over denominator cube root of q to the power of 4 end root end fraction. end cell end table$