Pertanyaan

Tentukan hasil pemangkatan bilangan berpangkat berikut ! d. ( 16 d 4 x a 4 b 8 ) 4 1 e. ( 64 b 3 x 27 a 6 ) − 3 1 f. ( − 27 c 6 d 9 x 8 a 3 b 6 ) − 3 2

Tentukan hasil pemangkatan bilangan berpangkat berikut !

d. $(\frac{a ^{4} b ^{8}}{16 d ^{4 x}})^{\frac{1}{4}}$
e. $(\frac{27 a ^{6}}{64 b ^{3 x}})^{- \frac{1}{3}}$
f. $(- \frac{8 a ^{3} b ^{6}}{27 c ^{6} d ^{9 x}})^{- \frac{2}{3}}$

D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

hasil pemangkatan dari , , dan .

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. Berdasarkan sifat-sifat di atas, maka: d) e) f) Dengan demikian, hasil pemangkatan dari , , dan .

Ingatlah sifat-sifat bilangan berpangkat berikut.

Berdasarkan sifat-sifat di atas, maka:

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

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

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