Pertanyaan

Sederhanakan operasi bilangan berpangkat berikut! a. ( a 4 3 × a − 8 3 ÷ a 6 1 ) 8 b. ( a 2 1 × a − 3 2 ÷ b 6 1 ) − 6

Sederhanakan operasi bilangan berpangkat berikut!

a. $(a^{\frac{3}{4}} \times a^{- \frac{3}{8}} \div a^{\frac{1}{6}})^{8}$
b. $(a^{\frac{1}{2}} \times a^{- \frac{2}{3}} \div b^{\frac{1}{6}})^{- 6}$

D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

bentuk sederhana dari , dan .

bentuk sederhana dari open parentheses a to the power of 3 over 4 end exponent cross times a to the power of negative 3 over 8 end exponent divided by a to the power of 1 over 6 end exponent close parentheses to the power of 8 equals a to the power of 5 over 3 end exponent

open parentheses a to the power of 3 over 4 end exponent cross times a to the power of negative 3 over 8 end exponent divided by a to the power of 1 over 6 end exponent close parentheses to the power of 8 equals a to the power of 5 over 3 end exponent

, dan

open parentheses a to the power of 1 half end exponent cross times a to the power of negative 2 over 3 end exponent divided by b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent equals a b

Pembahasan

Ingatlah sifat-sifat bilangan berpangkat berikut. Berdasarkan sifat-sifat di atas, maka: a) b) Dengan demikian, bentuk sederhana dari , dan .

Ingatlah sifat-sifat bilangan berpangkat berikut.

Berdasarkan sifat-sifat di atas, maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a to the power of 3 over 4 end exponent cross times a to the power of negative 3 over 8 end exponent divided by a to the power of 1 over 6 end exponent close parentheses to the power of 8 end cell equals cell open parentheses a to the power of 3 over 4 plus open parentheses negative 3 over 8 close parentheses minus 1 over 6 end exponent close parentheses to the power of 8 end cell row blank equals cell open parentheses a to the power of fraction numerator 18 minus 9 minus 4 over denominator 24 end fraction end exponent close parentheses to the power of 8 end cell row blank equals cell open parentheses a to the power of 5 over 24 end exponent close parentheses to the power of 8 end cell row blank equals cell a to the power of 5 over 24 cross times 8 end exponent end cell row blank equals cell a to the power of 40 over 24 end exponent end cell row blank equals cell a to the power of 5 over 3 end exponent end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a to the power of 1 half end exponent cross times a to the power of negative 2 over 3 end exponent divided by b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent end cell equals cell open parentheses a to the power of 1 half plus open parentheses negative 2 over 3 close parentheses end exponent divided by b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent end cell row blank equals cell open parentheses a to the power of fraction numerator 3 minus 4 over denominator 6 end fraction end exponent divided by b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent end cell row blank equals cell open parentheses a to the power of negative 1 over 6 end exponent divided by b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent end cell row blank equals cell open parentheses a to the power of negative 1 over 6 end exponent close parentheses to the power of negative 6 end exponent divided by open parentheses b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent end cell row blank equals cell a to the power of negative fraction numerator 1 over denominator up diagonal strike 6 end fraction cross times open parentheses negative up diagonal strike 6 close parentheses end exponent divided by b to the power of fraction numerator 1 over denominator up diagonal strike 6 end fraction cross times open parentheses negative up diagonal strike 6 close parentheses end exponent end cell row blank equals cell a divided by b to the power of negative 1 end exponent end cell row blank equals cell a divided by 1 over b end cell row blank equals cell a b end cell end table$

Dengan demikian, bentuk sederhana dari open parentheses a to the power of 3 over 4 end exponent cross times a to the power of negative 3 over 8 end exponent divided by a to the power of 1 over 6 end exponent close parentheses to the power of 8 equals a to the power of 5 over 3 end exponent , dan .