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Jika diketahui a=64,b=128danc=27, maka nilai dari 41​ab71​27a31​b72​c−32​​ adalah...

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Jika diketahui a equals 64 comma space b equals 128 space dan space c equals 27, maka nilai dari fraction numerator 27 a to the power of 1 third end exponent b to the power of 2 over 7 end exponent c to the power of negative begin display style 2 over 3 end style end exponent over denominator 1 fourth a b to the power of begin display style 1 over 7 end style end exponent end fraction adalah... 

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Berdasarkan sifat bilangan berpangkat a to the power of m divided by a to the power of n equals a to the power of m minus n end exponent maka

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 27 a to the power of 1 third end exponent b to the power of 2 over 7 end exponent c to the power of negative begin display style 2 over 3 end style end exponent over denominator 1 fourth a b to the power of begin display style 1 over 7 end style end exponent end fraction end cell equals cell fraction numerator 27 over denominator begin display style 1 fourth end style end fraction a to the power of 1 third minus 1 end exponent b to the power of 2 over 7 minus 1 over 7 end exponent c to the power of negative 2 over 3 end exponent end cell row blank equals cell open parentheses 27 divided by 1 fourth close parentheses open parentheses a to the power of 1 third minus 3 over 3 end exponent b to the power of 2 over 7 minus 1 over 7 end exponent c to the power of negative 2 over 3 end exponent close parentheses end cell row blank equals cell open parentheses 27 cross times 4 close parentheses open parentheses a to the power of negative 2 over 3 end exponent b to the power of 1 over 7 end exponent c to the power of negative 2 over 3 end exponent close parentheses end cell row blank equals cell 108 a to the power of negative 2 over 3 end exponent b to the power of 1 over 7 end exponent c to the power of negative 2 over 3 end exponent end cell end table

Berdasarkan sifat bilangan berpangkat a to the power of negative m end exponent equals 1 over a to the power of m maka

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 27 a to the power of 1 third end exponent b to the power of 2 over 7 end exponent c to the power of negative begin display style 2 over 3 end style end exponent over denominator 1 fourth a b to the power of begin display style 1 over 7 end style end exponent end fraction end cell equals cell fraction numerator 27 over denominator begin display style 1 fourth end style end fraction a to the power of 1 third minus 1 end exponent b to the power of 2 over 7 minus 1 over 7 end exponent c to the power of negative 2 over 3 end exponent end cell row blank equals cell open parentheses 27 divided by 1 fourth close parentheses open parentheses a to the power of 1 third minus 3 over 3 end exponent b to the power of 2 over 7 minus 1 over 7 end exponent c to the power of negative 2 over 3 end exponent close parentheses end cell row blank equals cell open parentheses 27 cross times 4 close parentheses open parentheses a to the power of negative 2 over 3 end exponent b to the power of 1 over 7 end exponent c to the power of negative 2 over 3 end exponent close parentheses end cell row blank equals cell 108 a to the power of negative 2 over 3 end exponent b to the power of 1 over 7 end exponent c to the power of negative 2 over 3 end exponent end cell row blank equals cell fraction numerator 108 b to the power of begin display style 1 over 7 end style end exponent over denominator a to the power of begin display style 2 over 3 end style end exponent c to the power of begin display style 2 over 3 end style end exponent end fraction end cell end table

Diketahui a equals 64 comma space b equals 128 space dan space c equals 27 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 27 a to the power of 1 third end exponent b to the power of 2 over 7 end exponent c to the power of negative begin display style 2 over 3 end style end exponent over denominator 1 fourth a b to the power of begin display style 1 over 7 end style end exponent end fraction end cell equals cell fraction numerator 27 over denominator begin display style 1 fourth end style end fraction a to the power of 1 third minus 1 end exponent b to the power of 2 over 7 minus 1 over 7 end exponent c to the power of negative 2 over 3 end exponent end cell row blank equals cell open parentheses 27 divided by 1 fourth close parentheses open parentheses a to the power of 1 third minus 3 over 3 end exponent b to the power of 2 over 7 minus 1 over 7 end exponent c to the power of negative 2 over 3 end exponent close parentheses end cell row blank equals cell open parentheses 27 cross times 4 close parentheses open parentheses a to the power of negative 2 over 3 end exponent b to the power of 1 over 7 end exponent c to the power of negative 2 over 3 end exponent close parentheses end cell row blank equals cell 108 a to the power of negative 2 over 3 end exponent b to the power of 1 over 7 end exponent c to the power of negative 2 over 3 end exponent end cell row blank equals cell fraction numerator 1 08 b to the power of begin display style 1 over 7 end style end exponent over denominator a to the power of begin display style 2 over 3 end style end exponent c to the power of begin display style 2 over 3 end style end exponent end fraction end cell row blank equals cell fraction numerator 108 open parentheses 128 close parentheses to the power of begin display style 1 over 7 end style end exponent over denominator open parentheses 64 close parentheses to the power of begin display style 2 over 3 end style end exponent open parentheses 27 close parentheses to the power of begin display style 2 over 3 end style end exponent end fraction end cell row blank equals cell fraction numerator 108 open parentheses 2 to the power of 7 close parentheses to the power of begin display style 1 over 7 end style end exponent over denominator open parentheses 4 cubed close parentheses to the power of begin display style 2 over 3 end style end exponent open parentheses 3 cubed close parentheses to the power of begin display style 2 over 3 end style end exponent end fraction end cell end table

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 fraction numerator 27 a to the power of 1 third end exponent b to the power of 2 over 7 end exponent c to the power of negative begin display style 2 over 3 end style end exponent over denominator 1 fourth a b to the power of begin display style 1 over 7 end style end exponent end fraction end cell equals cell fraction numerator 27 over denominator begin display style 1 fourth end style end fraction a to the power of 1 third minus 1 end exponent b to the power of 2 over 7 minus 1 over 7 end exponent c to the power of negative 2 over 3 end exponent end cell row blank equals cell open parentheses 27 divided by 1 fourth close parentheses open parentheses a to the power of 1 third minus 3 over 3 end exponent b to the power of 2 over 7 minus 1 over 7 end exponent c to the power of negative 2 over 3 end exponent close parentheses end cell row blank equals cell open parentheses 27 cross times 4 close parentheses open parentheses a to the power of negative 2 over 3 end exponent b to the power of 1 over 7 end exponent c to the power of negative 2 over 3 end exponent close parentheses end cell row blank equals cell 108 a to the power of negative 2 over 3 end exponent b to the power of 1 over 7 end exponent c to the power of negative 2 over 3 end exponent end cell row blank equals cell fraction numerator 1 08 b to the power of begin display style 1 over 7 end style end exponent over denominator a to the power of begin display style 2 over 3 end style end exponent c to the power of begin display style 2 over 3 end style end exponent end fraction end cell row blank equals cell fraction numerator 108 open parentheses 128 close parentheses to the power of begin display style 1 over 7 end style end exponent over denominator open parentheses 64 close parentheses to the power of begin display style 2 over 3 end style end exponent open parentheses 27 close parentheses to the power of begin display style 2 over 3 end style end exponent end fraction end cell row blank equals cell fraction numerator 108 open parentheses 2 to the power of 7 close parentheses to the power of begin display style 1 over 7 end style end exponent over denominator open parentheses 4 cubed close parentheses to the power of begin display style 2 over 3 end style end exponent open parentheses 3 cubed close parentheses to the power of begin display style 2 over 3 end style end exponent end fraction end cell row blank equals cell fraction numerator 108 cross times 2 to the power of 7 cross times begin display style 1 over 7 end style end exponent over denominator 4 to the power of 3 cross times begin display style 2 over 3 end style end exponent 3 to the power of 3 cross times begin display style 2 over 3 end style end exponent end fraction end cell row blank equals cell fraction numerator 108 cross times 2 to the power of 1 over denominator 4 to the power of 1 cross times 3 to the power of 1 end fraction end cell row blank equals cell fraction numerator 108 cross times 2 over denominator 4 cross times 3 end fraction end cell row blank equals cell 3 over 2 end cell end table

Dengan demikian, nilai dari fraction numerator 27 a to the power of 1 third end exponent b to the power of 2 over 7 end exponent c to the power of negative begin display style 2 over 3 end style end exponent over denominator 1 fourth a b to the power of begin display style 1 over 7 end style end exponent end fraction adalah 3 over 2.

Jawaban terverifikasi

Dijawab oleh:

R. Febrianti

Mahasiswa/Alumni Universitas Negeri Malang

Terakhir diupdate 18 Oktober 2021

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