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Tentukan hasil operasi pemangkatan berikut! c. (−3k1​)2×(−3k2​)3 d. (−132​)5÷(−131​)8

Pertanyaan

Tentukan hasil operasi pemangkatan berikut!
c. open parentheses negative fraction numerator 1 over denominator 3 k end fraction close parentheses squared cross times open parentheses negative fraction numerator 2 over denominator 3 k end fraction close parentheses cubed
d. open parentheses negative 1 2 over 3 close parentheses to the power of 5 divided by open parentheses negative 1 1 third close parentheses to the power of 8

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

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Jawaban

hasil dari open parentheses negative 1 2 over 3 close parentheses to the power of 5 divided by open parentheses negative 1 1 third close parentheses to the power of 8 adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative 27 over 256 end cell end table.

Pembahasan

c. Berdasarkan sifat bilangan berpangkat open parentheses a divided by b close parentheses to the power of m equals a to the power of m divided by b to the power of m maka open parentheses negative fraction numerator 1 over denominator 3 k end fraction close parentheses squared cross times open parentheses negative fraction numerator 2 over denominator 3 k end fraction close parentheses cubed diperoleh sebagai berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative fraction numerator 1 over denominator 3 k end fraction close parentheses squared cross times open parentheses negative fraction numerator 2 over denominator 3 k end fraction close parentheses cubed end cell equals cell open parentheses fraction numerator negative 1 over denominator 3 k end fraction close parentheses squared cross times open parentheses fraction numerator negative 2 over denominator 3 k end fraction close parentheses cubed end cell row blank equals cell open parentheses negative 1 close parentheses squared over open parentheses 3 k close parentheses squared cross times open parentheses negative 2 close parentheses cubed over open parentheses 3 k close parentheses cubed end cell end table

Berdasarkan sifat bilangan berpangkat 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 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative fraction numerator 1 over denominator 3 k end fraction close parentheses squared cross times open parentheses negative fraction numerator 2 over denominator 3 k end fraction close parentheses cubed end cell equals cell open parentheses negative 1 close parentheses squared over open parentheses 3 k close parentheses squared cross times open parentheses negative 2 close parentheses cubed over open parentheses 3 k close parentheses cubed end cell row blank equals cell fraction numerator open parentheses negative 1 close parentheses squared cross times open parentheses negative 2 close parentheses cubed over denominator open parentheses 3 k close parentheses to the power of 2 plus 3 end exponent end fraction end cell row blank equals cell fraction numerator open parentheses negative 1 close parentheses squared cross times open parentheses negative 2 close parentheses cubed over denominator open parentheses 3 k close parentheses to the power of 5 end fraction end cell end table

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

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative fraction numerator 1 over denominator 3 k end fraction close parentheses squared cross times open parentheses negative fraction numerator 2 over denominator 3 k end fraction close parentheses cubed end cell equals cell open parentheses negative 1 close parentheses squared over open parentheses 3 k close parentheses squared cross times open parentheses negative 2 close parentheses cubed over open parentheses 3 k close parentheses cubed end cell row blank equals cell fraction numerator open parentheses negative 1 close parentheses squared cross times open parentheses negative 2 close parentheses cubed over denominator open parentheses 3 k close parentheses to the power of 2 plus 3 end exponent end fraction end cell row blank equals cell fraction numerator open parentheses negative 1 close parentheses squared cross times open parentheses negative 2 close parentheses cubed over denominator open parentheses 3 k close parentheses to the power of 5 end fraction end cell row blank equals cell fraction numerator open parentheses negative 1 close parentheses squared cross times open parentheses negative 2 close parentheses cubed over denominator 3 to the power of 5 cross times k to the power of 5 end fraction end cell end table

Menurut aturan pemangkatan bilangan pokok negatif yaitu open parentheses negative a close parentheses to the power of m comma space m spacebilangan ganjil maka open parentheses negative a close parentheses to the power of m equals negative 1 cross times a to the power of m dan open parentheses negative a close parentheses to the power of m comma space m spacebilangan genap maka open parentheses negative a close parentheses to the power of m equals a to the power of m serta sifat bilangan berpangkat 1 to the power of m equals 1 maka diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative fraction numerator 1 over denominator 3 k end fraction close parentheses squared cross times open parentheses negative fraction numerator 2 over denominator 3 k end fraction close parentheses cubed end cell equals cell fraction numerator open parentheses negative 1 close parentheses squared cross times open parentheses negative 2 close parentheses cubed over denominator 3 to the power of 5 cross times k to the power of 5 end fraction end cell row blank equals cell fraction numerator 1 squared cross times open parentheses open parentheses negative 1 close parentheses cross times 2 cubed close parentheses over denominator 3 to the power of 5 cross times k to the power of 5 end fraction end cell row blank equals cell fraction numerator 1 cross times open parentheses negative 1 cross times 8 close parentheses over denominator 243 k to the power of 5 end fraction end cell row blank equals cell fraction numerator 1 cross times negative 8 over denominator 243 k to the power of 5 end fraction end cell row blank equals cell fraction numerator negative 8 over denominator 243 k to the power of 5 end fraction end cell row blank equals cell negative fraction numerator 8 over denominator 243 k to the power of 5 end fraction end cell end table

Jadi hasil dari open parentheses negative fraction numerator 1 over denominator 3 k end fraction close parentheses squared cross times open parentheses negative fraction numerator 2 over denominator 3 k end fraction close parentheses cubed adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative fraction numerator 8 over denominator 243 k to the power of 5 end fraction end cell end table.

d. Pecahan campuran negative 1 2 over 3 space text dan end text space minus 1 1 third dapat diubah menjadi pecahan senilai sebagai berikut

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 1 2 over 3 end cell equals cell fraction numerator 3 cross times negative 1 plus 2 over denominator 3 end fraction end cell row blank equals cell fraction numerator negative 3 plus 2 over denominator 3 end fraction end cell row blank equals cell fraction numerator negative 1 over denominator 3 end fraction end cell row cell negative 1 1 third end cell equals cell fraction numerator 3 cross times negative 1 plus 1 over denominator 3 end fraction end cell row blank equals cell fraction numerator negative 3 plus 1 over denominator 3 end fraction end cell row blank equals cell fraction numerator negative 2 over denominator 3 end fraction end cell end table

Berdasarkan sifat bilangan berpangkat open parentheses a divided by b close parentheses to the power of m equals a to the power of m divided by b to the power of m maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative 1 2 over 3 close parentheses to the power of 5 divided by open parentheses negative 1 1 third close parentheses to the power of 8 end cell equals cell open parentheses fraction numerator negative 1 over denominator 3 end fraction close parentheses to the power of 5 divided by open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses to the power of 8 end cell row blank equals cell open parentheses negative 1 close parentheses to the power of 5 over 3 to the power of 5 divided by open parentheses negative 2 close parentheses to the power of 8 over 3 to the power of 8 end cell row blank equals cell open parentheses negative 1 close parentheses to the power of 5 over 3 to the power of 5 cross times 3 to the power of 8 over open parentheses negative 2 close parentheses to the power of 8 end cell row blank equals cell fraction numerator open parentheses negative 1 close parentheses to the power of 5 cross times 3 to the power of 8 over denominator open parentheses negative 2 close parentheses to the power of 8 cross times 3 to the power of 5 end fraction end cell end table

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 open parentheses negative 1 2 over 3 close parentheses to the power of 5 divided by open parentheses negative 1 1 third close parentheses to the power of 8 end cell equals cell open parentheses fraction numerator negative 1 over denominator 3 end fraction close parentheses to the power of 5 divided by open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses to the power of 8 end cell row blank equals cell fraction numerator open parentheses negative 1 close parentheses to the power of 5 cross times 3 to the power of 8 over denominator open parentheses negative 2 close parentheses to the power of 8 cross times 3 to the power of 5 end fraction end cell row blank equals cell fraction numerator open parentheses negative 1 close parentheses to the power of 5 cross times 3 to the power of 8 minus 5 end exponent over denominator open parentheses negative 2 close parentheses to the power of 8 end fraction end cell row blank equals cell fraction numerator open parentheses negative 1 close parentheses to the power of 5 cross times 3 cubed over denominator open parentheses negative 2 close parentheses to the power of 8 end fraction end cell end table

Menurut aturan pemangkatan bilangan pokok negatif yaitu open parentheses negative a close parentheses to the power of m comma space m spacebilangan ganjil maka open parentheses negative a close parentheses to the power of m equals negative 1 cross times a to the power of m dan open parentheses negative a close parentheses to the power of m comma space m spacebilangan genap maka open parentheses negative a close parentheses to the power of m equals a to the power of m serta sifat bilangan berpangkat 1 to the power of m equals 1 sehingga diperoleh 

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative 1 2 over 3 close parentheses to the power of 5 divided by open parentheses negative 1 1 third close parentheses to the power of 8 end cell equals cell open parentheses fraction numerator negative 1 over denominator 3 end fraction close parentheses to the power of 5 divided by open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses to the power of 8 end cell row blank equals cell fraction numerator open parentheses negative 1 close parentheses to the power of 5 cross times 3 to the power of 8 over denominator open parentheses negative 2 close parentheses to the power of 8 cross times 3 to the power of 5 end fraction end cell row blank equals cell fraction numerator open parentheses negative 1 close parentheses to the power of 5 cross times 3 to the power of 8 minus 5 end exponent over denominator open parentheses negative 2 close parentheses to the power of 8 end fraction end cell row blank equals cell fraction numerator open parentheses negative 1 close parentheses to the power of 5 cross times 3 cubed over denominator open parentheses negative 2 close parentheses to the power of 8 end fraction end cell row blank equals cell fraction numerator negative 1 cross times 1 to the power of 5 cross times 3 cubed over denominator 2 to the power of 8 end fraction end cell row blank equals cell fraction numerator negative 1 cross times 1 cross times 27 over denominator 256 end fraction end cell row blank equals cell fraction numerator negative 1 cross times 27 over denominator 256 end fraction end cell row blank equals cell fraction numerator negative 27 over denominator 256 end fraction end cell row blank equals cell negative 27 over 256 end cell end table

Jadi hasil dari open parentheses negative 1 2 over 3 close parentheses to the power of 5 divided by open parentheses negative 1 1 third close parentheses to the power of 8 adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell negative 27 over 256 end cell end table.

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