Pertanyaan

Sederhanakan akar-akar bilangan berikut ! d. 3 − 729 a 6 e. 3 − 27 a 9 b − 12 f. 2 3 8 x 6 y − 3 z 4

Sederhanakan akar-akar bilangan berikut !

d. $3 - 729 a^{6}$
e. $3 - 27 a^{9} b^{- 12}$
f. $2 3 8 x^{6} y^{- 3} z^{4}$

D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

hasil dari , , dan .

hasil dari Error converting from MathML to accessible text.

, $cube root of negative 27 a to the power of 9 b to the power of negative 12 end exponent end root equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 a cubed over denominator b to the power of 4 end fraction end cell end table$ , dan $2 cube root of 8 x to the power of 6 y to the power of negative 3 end exponent z to the power of 4 end root equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 4 x squared z cube root of z over denominator y end fraction end cell end table$ .

Pembahasan

Ingatlah, jika hasil pemangkatan , maka nilai . Ingat juga sifat-sifat bilangan berpangkat sebagai berikut. Berdasarkan hal-hal di atas, maka: d) e) f) 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:

$table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of negative 27 a to the power of 9 b to the power of negative 12 end exponent end root end cell equals cell cube root of negative 3 cubed a to the power of 9 b to the power of negative 12 end exponent end root end cell row blank equals cell cube root of open parentheses negative 3 a cubed b to the power of negative 4 end exponent close parentheses cubed end root end cell row blank equals cell negative 3 a cubed b to the power of negative 4 end exponent end cell row blank equals cell negative fraction numerator 3 a cubed over denominator b to the power of 4 end fraction end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell 2 cube root of 8 x to the power of 6 y to the power of negative 3 end exponent z to the power of 4 end root end cell equals cell 2 space cube root of open parentheses 2 x squared y to the power of negative 1 end exponent z to the power of 4 over 3 end exponent close parentheses cubed end root end cell row blank equals cell 2 times open parentheses 2 x squared y to the power of negative 1 end exponent z to the power of 4 over 3 end exponent close parentheses end cell row blank equals cell 4 x squared y to the power of negative 1 end exponent z to the power of 4 over 3 end exponent end cell row blank equals cell fraction numerator 4 x squared z to the power of 4 over 3 end exponent over denominator y end fraction end cell row blank equals cell fraction numerator 4 x squared z times z to the power of begin display style 1 third end style end exponent over denominator y end fraction end cell row blank equals cell fraction numerator 4 x squared z cube root of z over denominator y end fraction end cell end table$

Dengan demikian, hasil dari Error converting from MathML to accessible text. , $cube root of negative 27 a to the power of 9 b to the power of negative 12 end exponent end root equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 a cubed over denominator b to the power of 4 end fraction end cell end table$ , dan $2 cube root of 8 x to the power of 6 y to the power of negative 3 end exponent z to the power of 4 end root equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 4 x squared z cube root of z over denominator y end fraction end cell end table$ .