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Tentukan hasil pemangkatan berikut! g. − 8 1 − 4 3 ​ h. ( 27 a 3 8 ​ ) − 3 2 ​

Tentukan hasil pemangkatan berikut!

g.
h.

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D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

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hasil dari adalah dan hasil dari adalah .

hasil dari negative 81 to the power of negative 3 over 4 end exponent adalah 1 over 27 dan hasil dari open parentheses fraction numerator 8 over denominator 27 a cubed end fraction close parentheses to the power of negative 2 over 3 end exponent adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 9 a squared over denominator 4 end fraction end cell end table.

Pembahasan

Ingatlah untuk sembarang bilangan dengan , berlaku sifat-sifat berikut. Berdasarkan sifat-sifat di atas, maka: g) h) Dengan demikian, hasil dari adalah dan hasil dari adalah .

Ingatlah untuk sembarang bilangan a dengan a not equal to 0, berlaku sifat-sifat berikut.

left parenthesis straight i right parenthesis space a to the power of m over n end exponent equals n-th root of a to the power of m end root space space atau space space a to the power of m over n end exponent equals open parentheses n-th root of a close parentheses to the power of straight m left parenthesis ii right parenthesis space a to the power of negative m end exponent equals 1 over a to the power of m left parenthesis iii right parenthesis space 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 left parenthesis iv right parenthesis space a to the power of m over b to the power of m equals open parentheses a over b close parentheses to the power of m left parenthesis v right parenthesis space a to the power of m b to the power of m equals left parenthesis a b right parenthesis to the power of m  

Berdasarkan sifat-sifat di atas, maka:

g)

table attributes columnalign right center left columnspacing 0px end attributes row cell negative 81 to the power of negative 3 over 4 end exponent end cell equals cell negative 1 over 81 to the power of begin display style 3 over 4 end style end exponent end cell row blank equals cell negative fraction numerator 1 over denominator fourth root of 81 cubed end root end fraction end cell row blank equals cell negative fraction numerator 1 over denominator fourth root of open parentheses 3 to the power of 4 close parentheses cubed end root end fraction end cell row blank equals cell negative fraction numerator 1 over denominator fourth root of 3 to the power of 4 cross times 3 end exponent end root end fraction end cell row blank equals cell negative fraction numerator 1 over denominator fourth root of 3 to the power of 12 end root end fraction end cell row blank equals cell negative 1 over 3 to the power of begin display style 12 over 4 end style end exponent end cell row blank equals cell negative 1 over 3 cubed end cell row blank equals cell negative 1 over 27 end cell end table

h)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 8 over denominator 27 a cubed end fraction close parentheses to the power of negative 2 over 3 end exponent end cell equals cell 1 over open parentheses fraction numerator 8 over denominator 27 a cubed end fraction close parentheses to the power of begin display style 2 over 3 end style end exponent end cell row blank equals cell fraction numerator 1 over denominator cube root of open parentheses fraction numerator 8 over denominator 27 a cubed end fraction close parentheses squared end root end fraction end cell row blank equals cell fraction numerator 1 over denominator cube root of fraction numerator 8 squared over denominator 27 squared a to the power of 3 cross times 2 end exponent end fraction end root end fraction end cell row blank equals cell fraction numerator 1 over denominator cube root of begin display style fraction numerator 64 over denominator 729 a to the power of 6 end fraction end style end root end fraction end cell row blank equals cell fraction numerator 1 over denominator cube root of begin display style 4 cubed over left parenthesis 9 a squared right parenthesis cubed end style end root end fraction end cell row blank equals cell fraction numerator 1 over denominator cube root of open parentheses begin display style fraction numerator 4 over denominator 9 a squared end fraction end style close parentheses cubed end root end fraction end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator 4 over denominator 9 a squared end fraction end style end fraction end cell row blank equals cell fraction numerator 9 a squared over denominator 4 end fraction end cell end table   

Dengan demikian, hasil dari negative 81 to the power of negative 3 over 4 end exponent adalah 1 over 27 dan hasil dari open parentheses fraction numerator 8 over denominator 27 a cubed end fraction close parentheses to the power of negative 2 over 3 end exponent adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 9 a squared over denominator 4 end fraction end cell end table.

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