Pertanyaan

Sederhanakan operasi bilangan berpangkat berikut! c. ( x 4 1 ) − 8 × ( x 3 2 ) 4 3 × ( x 5 3 ) − 4 5 d. ( x 3 1 ) 4 6 × ( x 3 2 ) − 1 4 3 × ( x 8 5 ) − 5 8

Sederhanakan operasi bilangan berpangkat berikut!

c. $(x^{\frac{1}{4}})^{- 8} \times (x^{\frac{2}{3}})^{\frac{3}{4}} \times (x^{\frac{3}{5}})^{- \frac{5}{4}}$
d. $(x^{\frac{1}{3}})^{\frac{6}{4}} \times (x^{\frac{2}{3}})^{- 1 \frac{3}{4}} \times (x^{\frac{5}{8}})^{- \frac{8}{5}}$

D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

bentuk sederhana dari , dan .

bentuk sederhana dari

open parentheses x to the power of 1 fourth end exponent close parentheses to the power of negative 8 end exponent cross times open parentheses x to the power of 2 over 3 end exponent close parentheses to the power of 3 over 4 end exponent cross times open parentheses x to the power of 3 over 5 end exponent close parentheses to the power of negative 5 over 4 end exponent equals 1 over x to the power of begin display style 9 over 4 end style end exponent

, dan

open parentheses x to the power of 1 third end exponent close parentheses to the power of 6 over 4 end exponent space cross times space open parentheses x to the power of 2 over 3 end exponent close parentheses to the power of negative 1 3 over 4 end exponent space cross times space open parentheses x to the power of 5 over 8 end exponent close parentheses to the power of negative 8 over 5 end exponent equals 1 over x to the power of begin display style 5 over 3 end style end exponent

Pembahasan

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

Ingatlah sifat-sifat bilangan berpangkat berikut.

Berdasarkan sifat-sifat di atas, maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses x to the power of 1 fourth end exponent close parentheses to the power of negative 8 end exponent cross times open parentheses x to the power of 2 over 3 end exponent close parentheses to the power of 3 over 4 end exponent cross times open parentheses x to the power of 3 over 5 end exponent close parentheses to the power of negative 5 over 4 end exponent end cell equals cell x to the power of 1 fourth cross times open parentheses negative 8 close parentheses end exponent times x to the power of fraction numerator 2 over denominator up diagonal strike 3 end fraction cross times fraction numerator up diagonal strike 3 over denominator 4 end fraction end exponent times x to the power of fraction numerator 3 over denominator up diagonal strike 5 end fraction cross times open parentheses negative fraction numerator up diagonal strike 5 over denominator 4 end fraction close parentheses end exponent end cell row blank equals cell x to the power of negative 2 end exponent times x to the power of 2 over 4 end exponent times x to the power of negative 3 over 4 end exponent end cell row blank equals cell x to the power of negative 2 plus 1 half plus open parentheses negative 3 over 4 close parentheses end exponent end cell row blank equals cell x to the power of fraction numerator negative 8 plus 2 minus 3 over denominator 4 end fraction end exponent end cell row blank equals cell x to the power of negative 9 over 4 end exponent end cell row blank equals cell 1 over x to the power of begin display style 9 over 4 end style end exponent end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses x to the power of 1 third end exponent close parentheses to the power of 6 over 4 end exponent space cross times space open parentheses x to the power of 2 over 3 end exponent close parentheses to the power of negative 1 3 over 4 end exponent space cross times space open parentheses x to the power of 5 over 8 end exponent close parentheses to the power of negative 8 over 5 end exponent end cell equals cell x to the power of 1 third cross times 6 over 4 end exponent times x to the power of 2 over 3 cross times open parentheses negative 7 over 4 close parentheses end exponent times x to the power of 5 over 8 cross times open parentheses negative 8 over 5 close parentheses end exponent end cell row blank equals cell x to the power of 6 over 12 end exponent times x to the power of negative 14 over 12 end exponent times x to the power of negative 1 end exponent end cell row blank equals cell x to the power of 1 half plus open parentheses negative 7 over 6 close parentheses plus open parentheses negative 1 close parentheses end exponent end cell row blank equals cell x to the power of fraction numerator 3 minus 7 minus 6 over denominator 6 end fraction end exponent end cell row blank equals cell x to the power of negative 10 over 6 end exponent end cell row blank equals cell x to the power of negative 5 over 3 end exponent end cell row blank equals cell 1 over x to the power of begin display style 5 over 3 end style end exponent end cell end table$

Dengan demikian, bentuk sederhana dari , dan .