Pertanyaan

Tentukan hasil operasi bilanganberikut dalam bentuk akar! b. ( m 2 n − 3 2 ) 3

Tentukan hasil operasi bilangan berikut dalam bentuk akar!
b. $(m^{2} n^{- \frac{2}{3}})^{3}$

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Berdasarkan sifat bilangan berpangkat maka diperoleh sebagai berikut. Berdasarkan sifat bilangan berpangkat maka Berdasarkan sifat bilangan berpangkat maka Berdasarkan sifat bilangan berpangkat pecahan yaitu maka Jadi hasil operasi bilangan dalam bentuk akar adalah .

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 open parentheses m squared n to the power of negative 2 over 3 end exponent close parentheses cubed diperoleh sebagai berikut.

open parentheses m squared n to the power of negative 2 over 3 end exponent close parentheses cubed equals open parentheses m squared close parentheses cubed open parentheses n to the power of negative 2 over 3 end exponent close parentheses cubed

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

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

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

Jadi hasil operasi bilangan open parentheses m squared n to the power of negative 2 over 3 end exponent close parentheses cubed dalam bentuk akar adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of m to the power of 12 over n to the power of 4 end root end cell end table .