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Pertanyaan

Tentukan hasil operasi bilangan berikut dalam bentuk akar!
b. open parentheses m squared n to the power of negative 2 over 3 end exponent close parentheses cubed

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

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

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 end table

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 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 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

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.
 

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