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Pertanyaan

Tentukan hasil pemangkatan berikut!

d. open parentheses negative 5 a to the power of negative 2 end exponent close parentheses to the power of negative 3 end exponent
e. open parentheses 2 a squared b cubed close parentheses to the power of negative 6 end exponent
f. open parentheses 3 a cubed b to the power of negative 4 end exponent close parentheses to the power of negative 5 end exponent

D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

hasil dari  open parentheses negative 5 a to the power of negative 2 end exponent close parentheses to the power of negative 3 end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a to the power of 6 over 125 end cell end table, open parentheses 2 a squared b cubed close parentheses to the power of negative 6 end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator 64 a to the power of 12 b to the power of 18 end fraction end cell end table, dan open parentheses 3 a cubed b to the power of negative 4 end exponent close parentheses to the power of negative 5 end exponent equals fraction numerator b to the power of 20 over denominator 243 a to the power of 15 end fraction.

Pembahasan

Ingatlah sifat-sifat bilangan berpangkat berikut.

left parenthesis straight i right parenthesis space 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 left parenthesis ii 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 iii right parenthesis space open parentheses a b close parentheses to the power of m equals a to the power of m b to the power of m left parenthesis iv right parenthesis space 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 left parenthesis straight v right parenthesis space a to the power of negative m end exponent equals 1 over a to the power of m left parenthesis vi right parenthesis space open parentheses negative a close parentheses to the power of m equals negative a to the power of m space space untuk space m space bil. ganjil  

Berdasarkan sifat-sifat di atas, maka:

d)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative 5 a to the power of negative 2 end exponent close parentheses to the power of negative 3 end exponent end cell equals cell 1 over open parentheses negative 5 a to the power of negative 2 end exponent close parentheses cubed end cell row blank equals cell 1 over open parentheses negative begin display style 5 over a squared end style close parentheses cubed end cell row blank equals cell fraction numerator 1 over denominator open parentheses negative 5 over a squared close parentheses cross times open parentheses negative 5 over a squared close parentheses cross times open parentheses negative 5 over a squared close parentheses end fraction end cell row blank equals cell fraction numerator 1 over denominator negative begin display style 125 over a to the power of 2 plus 2 plus 2 end exponent end style end fraction end cell row blank equals cell fraction numerator 1 over denominator negative begin display style 125 over a to the power of 6 end style end fraction end cell row blank equals cell negative a to the power of 6 over 125 end cell end table

e)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 2 a squared b cubed close parentheses to the power of negative 6 end exponent end cell equals cell 1 over open parentheses 2 a squared b cubed close parentheses to the power of 6 end cell row blank equals cell fraction numerator 1 over denominator 2 to the power of 6 cross times open parentheses a squared close parentheses to the power of 6 cross times open parentheses b cubed close parentheses to the power of 6 end fraction end cell row blank equals cell fraction numerator 1 over denominator 64 cross times a to the power of 2 cross times 6 end exponent cross times b to the power of 3 cross times 6 end exponent end fraction end cell row blank equals cell fraction numerator 1 over denominator 64 cross times a to the power of 12 cross times b to the power of 18 end fraction end cell row blank equals cell fraction numerator 1 over denominator 64 a to the power of 12 b to the power of 18 end fraction end cell end table

f)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 a cubed b to the power of negative 4 end exponent close parentheses to the power of negative 5 end exponent end cell equals cell 1 over open parentheses 3 a cubed b to the power of negative 4 end exponent close parentheses to the power of 5 end cell row blank equals cell 1 over open parentheses begin display style fraction numerator 3 a cubed over denominator b to the power of 4 end fraction end style close parentheses to the power of 5 end cell row blank equals cell fraction numerator 1 over denominator begin display style open parentheses 3 a cubed close parentheses to the power of 5 over open parentheses b to the power of 4 close parentheses to the power of 5 end style end fraction end cell row blank equals cell open parentheses b to the power of 4 close parentheses to the power of 5 over open parentheses 3 a cubed close parentheses to the power of 5 end cell row blank equals cell fraction numerator b to the power of 20 over denominator 3 to the power of 5 a to the power of 15 end fraction end cell row blank equals cell fraction numerator b to the power of 20 over denominator 243 a to the power of 15 end fraction end cell end table

Dengan demikian, hasil dari  open parentheses negative 5 a to the power of negative 2 end exponent close parentheses to the power of negative 3 end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell a to the power of 6 over 125 end cell end table, open parentheses 2 a squared b cubed close parentheses to the power of negative 6 end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator 64 a to the power of 12 b to the power of 18 end fraction end cell end table, dan open parentheses 3 a cubed b to the power of negative 4 end exponent close parentheses to the power of negative 5 end exponent equals fraction numerator b to the power of 20 over denominator 243 a to the power of 15 end fraction.

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