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Tentukan hasil pemangkatan bilangan berpangkat berikut ! a. (4654​)23​ b. (5649​)−31​ c. (−2834​)−43​

Pertanyaan

Tentukan hasil pemangkatan bilangan berpangkat berikut !

a. open parentheses 5 to the power of 4 over 4 to the power of 6 close parentheses to the power of 3 over 2 end exponent
b. open parentheses 4 to the power of 9 over 5 to the power of 6 close parentheses to the power of negative 1 third end exponent
c. open parentheses negative 3 to the power of 4 over 2 to the power of 8 close parentheses to the power of negative 3 over 4 end exponent

D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

hasil pemangkatan dari  open parentheses 5 to the power of 4 over 4 to the power of 6 close parentheses to the power of 3 over 2 end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 to the power of 6 over 4 to the power of 9 end cell end table, open parentheses 4 to the power of 9 over 5 to the power of 6 close parentheses to the power of negative 1 third end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 25 over 64 end cell end table, dan open parentheses negative 3 to the power of 4 over 2 to the power of 8 close parentheses to the power of negative 3 over 4 end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 64 over denominator 27 times open parentheses negative 1 close parentheses to the power of 3 over 4 end exponent end fraction end cell end table.

Pembahasan

Ingatlah sifat-sifat bilangan berpangkat berikut.

left parenthesis straight i right parenthesis space 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 left parenthesis ii 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 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 negative m end exponent equals 1 over a to the power of m  

Berdasarkan sifat-sifat di atas, maka:

a)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 5 to the power of 4 over 4 to the power of 6 close parentheses to the power of 3 over 2 end exponent end cell equals cell open parentheses 5 to the power of 4 close parentheses to the power of begin display style 3 over 2 end style end exponent over open parentheses 4 to the power of 6 close parentheses to the power of begin display style 3 over 2 end style end exponent end cell row blank equals cell 5 to the power of 4 cross times begin display style 3 over 2 end style end exponent over 4 to the power of 6 cross times begin display style 3 over 2 end style end exponent end cell row blank equals cell 5 to the power of begin display style 12 over 2 end style end exponent over 4 to the power of begin display style 18 over 2 end style end exponent end cell row blank equals cell 5 to the power of 6 over 4 to the power of 9 end cell end table

b)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 4 to the power of 9 over 5 to the power of 6 close parentheses to the power of negative 1 third end exponent end cell equals cell open parentheses 4 to the power of 9 close parentheses to the power of negative begin display style 1 third end style end exponent over open parentheses 5 to the power of 6 close parentheses to the power of negative begin display style 1 third end style end exponent end cell row blank equals cell 4 to the power of 9 cross times open parentheses negative begin display style 1 third end style close parentheses end exponent over 5 to the power of 6 cross times open parentheses negative begin display style 1 third end style close parentheses end exponent end cell row blank equals cell 4 to the power of negative 3 end exponent over 5 to the power of negative 2 end exponent end cell row blank equals cell fraction numerator begin display style 1 over 4 cubed end style over denominator begin display style 1 over 5 squared end style end fraction end cell row blank equals cell 5 squared over 4 cubed end cell row blank equals cell 25 over 64 end cell end table

c)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses negative 3 to the power of 4 over 2 to the power of 8 close parentheses to the power of negative 3 over 4 end exponent end cell equals cell open parentheses open parentheses negative 1 close parentheses times 3 to the power of 4 over 2 to the power of 8 close parentheses to the power of negative 3 over 4 end exponent end cell row blank equals cell open parentheses negative 1 close parentheses to the power of negative 3 over 4 end exponent times open parentheses 3 to the power of 4 over 2 to the power of 8 close parentheses to the power of negative 3 over 4 end exponent end cell row blank equals cell 1 over open parentheses negative 1 close parentheses to the power of begin display style 3 over 4 end style end exponent times open parentheses 3 to the power of 4 close parentheses to the power of negative begin display style 3 over 4 end style end exponent over open parentheses 2 to the power of 8 close parentheses to the power of negative begin display style 3 over 4 end style end exponent end cell row blank equals cell fraction numerator 3 to the power of up diagonal strike 4 cross times open parentheses negative begin display style fraction numerator 3 over denominator up diagonal strike 4 end fraction end style close parentheses end exponent over denominator open parentheses negative 1 close parentheses to the power of 3 over 4 end exponent times 2 to the power of 8 cross times open parentheses negative begin display style 3 over 4 end style close parentheses end exponent end fraction end cell row blank equals cell fraction numerator 3 to the power of negative 3 end exponent over denominator open parentheses negative 1 close parentheses to the power of 3 over 4 end exponent times 2 to the power of negative begin display style 24 over 4 end style end exponent end fraction end cell row blank equals cell fraction numerator begin display style 1 over 3 cubed end style over denominator open parentheses negative 1 close parentheses to the power of 3 over 4 end exponent times 2 to the power of negative 6 end exponent end fraction end cell row blank equals cell fraction numerator begin display style 1 over 27 end style over denominator open parentheses negative 1 close parentheses to the power of 3 over 4 end exponent over 2 to the power of 6 end fraction end cell row blank equals cell fraction numerator 2 to the power of 6 over denominator 27 times open parentheses negative 1 close parentheses to the power of 3 over 4 end exponent end fraction end cell row blank equals cell fraction numerator 64 over denominator 27 times open parentheses negative 1 close parentheses to the power of 3 over 4 end exponent end fraction end cell end table

Dengan demikian, hasil pemangkatan dari  open parentheses 5 to the power of 4 over 4 to the power of 6 close parentheses to the power of 3 over 2 end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 5 to the power of 6 over 4 to the power of 9 end cell end table, open parentheses 4 to the power of 9 over 5 to the power of 6 close parentheses to the power of negative 1 third end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 25 over 64 end cell end table, dan open parentheses negative 3 to the power of 4 over 2 to the power of 8 close parentheses to the power of negative 3 over 4 end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 64 over denominator 27 times open parentheses negative 1 close parentheses to the power of 3 over 4 end exponent end fraction end cell end table.

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