Tentukan hasil pemangkatan bilangan berpangkat berikut ! d. (16d4xa4b8​)41​ e. (64b3x27a6​)−31​ f. (−27c6d9x8a3b6​)−32​

Pertanyaan

Tentukan hasil pemangkatan bilangan berpangkat berikut !

d. open parentheses fraction numerator a to the power of 4 b to the power of 8 over denominator 16 d to the power of 4 x end exponent end fraction close parentheses to the power of 1 fourth end exponent
e. open parentheses fraction numerator 27 a to the power of 6 over denominator 64 b to the power of 3 x end exponent end fraction close parentheses to the power of negative 1 third end exponent
f. open parentheses negative fraction numerator 8 a cubed b to the power of 6 over denominator 27 c to the power of 6 d to the power of 9 x end exponent end fraction close parentheses to the power of negative 2 over 3 end exponent

D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

hasil pemangkatan dari  open parentheses fraction numerator a to the power of 4 b to the power of 8 over denominator 16 d to the power of 4 x end exponent end fraction close parentheses to the power of 1 fourth end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator a b squared over denominator 2 d to the power of x end fraction end cell end table , open parentheses fraction numerator 27 a to the power of 6 over denominator 64 b to the power of 3 x end exponent end fraction 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 fraction numerator 4 b to the power of x over denominator 3 a squared end fraction end cell end table, dan open parentheses negative fraction numerator 8 a cubed b to the power of 6 over denominator 27 c to the power of 6 d to the power of 9 x end exponent end fraction close parentheses to the power of negative 2 over 3 end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 9 c to the power of 4 d to the power of 6 x end exponent over denominator 4 a squared b to the power of 4 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:

d)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator a to the power of 4 b to the power of 8 over denominator 16 d to the power of 4 x end exponent end fraction close parentheses to the power of 1 fourth end exponent end cell equals cell open parentheses a to the power of 4 b to the power of 8 close parentheses to the power of begin display style 1 fourth end style end exponent over open parentheses 16 d to the power of 4 x end exponent close parentheses to the power of begin display style 1 fourth end style end exponent end cell row blank equals cell fraction numerator open parentheses a to the power of 4 close parentheses to the power of begin display style 1 fourth end style end exponent times open parentheses b to the power of 8 close parentheses to the power of begin display style 1 fourth end style end exponent over denominator open parentheses 16 close parentheses to the power of begin display style 1 fourth end style end exponent times open parentheses d to the power of 4 x end exponent close parentheses to the power of begin display style 1 fourth end style end exponent end fraction end cell row blank equals cell fraction numerator a to the power of 4 cross times begin display style 1 fourth end style end exponent b to the power of 8 cross times begin display style 1 fourth end style end exponent over denominator 2 to the power of up diagonal strike 4 cross times begin display style fraction numerator 1 over denominator up diagonal strike 4 end fraction end style end exponent d to the power of up diagonal strike 4 x times begin display style fraction numerator 1 over denominator up diagonal strike 4 end fraction end style end exponent end fraction end cell row blank equals cell fraction numerator a b squared over denominator 2 d to the power of x end fraction end cell end table

e)

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

f)

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

Dengan demikian, hasil pemangkatan dari  open parentheses fraction numerator a to the power of 4 b to the power of 8 over denominator 16 d to the power of 4 x end exponent end fraction close parentheses to the power of 1 fourth end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator a b squared over denominator 2 d to the power of x end fraction end cell end table , open parentheses fraction numerator 27 a to the power of 6 over denominator 64 b to the power of 3 x end exponent end fraction 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 fraction numerator 4 b to the power of x over denominator 3 a squared end fraction end cell end table, dan open parentheses negative fraction numerator 8 a cubed b to the power of 6 over denominator 27 c to the power of 6 d to the power of 9 x end exponent end fraction close parentheses to the power of negative 2 over 3 end exponent equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 9 c to the power of 4 d to the power of 6 x end exponent over denominator 4 a squared b to the power of 4 end fraction end cell end table.

118

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