Pertanyaan

Sederhanakan akar-akar bilangan berikut ! g. 4 81 m 8 n − 4 h. 5 4 m 4 n − 12 x 6

Sederhanakan akar-akar bilangan berikut !

g. $4 81 m^{8} n^{- 4}$
h. $5 4 m^{4} n^{- 12} x^{6}$

D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

hasil dari , dan .

hasil dari $fourth root of 81 m to the power of 8 n to the power of negative 4 end exponent end root equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 m squared over denominator n end fraction end cell end table$ , dan $5 fourth root of m to the power of 4 n to the power of negative 12 end exponent x to the power of 6 end root equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 5 m x square root of x over denominator n cubed end fraction end cell end table$ .

Pembahasan

Ingatlah, jika hasil pemangkatan , maka nilai . Ingat juga sifat-sifat bilangan berpangkat sebagai berikut. Berdasarkan hal-hal di atas, maka: g) h) Dengan demikian, hasil dari , dan .

Ingatlah, jika hasil pemangkatan a to the power of n equals b , maka nilai n-th root of b equals n-th root of a to the power of n end root equals a .

Ingat juga sifat-sifat bilangan berpangkat sebagai berikut.

open parentheses straight i close parentheses space a to the power of negative m end exponent equals 1 over a to the power of m open parentheses ii close parentheses space 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

Berdasarkan hal-hal di atas, maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fourth root of 81 m to the power of 8 n to the power of negative 4 end exponent end root end cell equals cell fourth root of 3 to the power of 4 m to the power of 8 n to the power of negative 4 end exponent end root end cell row blank equals cell fourth root of open parentheses 3 m squared n to the power of negative 1 end exponent close parentheses to the power of 4 end root end cell row blank equals cell 3 m squared n to the power of negative 1 end exponent end cell row blank equals cell fraction numerator 3 m squared over denominator n end fraction end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell 5 fourth root of m to the power of 4 n to the power of negative 12 end exponent x to the power of 6 end root end cell equals cell 5 space fourth root of open parentheses m n to the power of negative 3 end exponent x to the power of 6 over 4 end exponent close parentheses to the power of 4 end root end cell row blank equals cell 5 times open parentheses m n to the power of negative 3 end exponent x to the power of 6 over 4 end exponent close parentheses end cell row blank equals cell 5 m n to the power of negative 3 end exponent x to the power of 3 over 2 end exponent end cell row blank equals cell fraction numerator 5 m times x times x to the power of begin display style 1 half end style end exponent over denominator n cubed end fraction end cell row blank equals cell fraction numerator 5 m x square root of x over denominator n cubed end fraction end cell end table$

Dengan demikian, hasil dari $fourth root of 81 m to the power of 8 n to the power of negative 4 end exponent end root equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 m squared over denominator n end fraction end cell end table$ , dan $5 fourth root of m to the power of 4 n to the power of negative 12 end exponent x to the power of 6 end root equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 5 m x square root of x over denominator n cubed end fraction end cell end table$ .