Pertanyaan

⎝ ⎛ 3 1 ( 3 1 ( 3 2 ) 2 ) 2 2 1 ( 2 1 ( 2 2 ) 3 ) 3 ⎠ ⎞ − 2 1 = ....

$⎝ ⎛ \frac{\frac{1}{2} ( \frac{1}{2} ( 2 ^{2} ) 3 ) 3}{\frac{1}{3} ( \frac{1}{3} ( 3 ^{2} ) 2 ) 2} ⎠ ⎞^{- \frac{1}{2}} = ....$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Jika diberikanbilangan riil danbilangan rasional maka berlaku sifatberikut. Sehingga dapat ditentukan hasil dari bentuk berikut. Sehingga diperoleh . Jadi, jawaban yang benar adalah C.

Jika diberikan bilangan riil dan bilangan rasional p space dan space q maka berlaku sifat berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a to the power of p close parentheses to the power of q end cell equals cell a to the power of p q end exponent end cell row cell a to the power of negative p end exponent end cell equals cell 1 over a to the power of p end cell end table

Sehingga dapat ditentukan hasil dari bentuk berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator begin display style 1 half open parentheses 1 half open parentheses 2 squared close parentheses 3 close parentheses 3 end style over denominator begin display style 1 third open parentheses 1 third open parentheses 3 squared close parentheses 2 close parentheses 2 end style end fraction close parentheses to the power of negative 1 half end exponent end cell equals cell open parentheses fraction numerator begin display style 1 half open parentheses 1 half open parentheses 4 close parentheses 3 close parentheses 3 end style over denominator begin display style 1 third open parentheses 1 third open parentheses 9 close parentheses 2 close parentheses 2 end style end fraction close parentheses to the power of negative 1 half end exponent end cell row blank equals cell open parentheses fraction numerator begin display style 1 half open parentheses 12 over 2 close parentheses 3 end style over denominator begin display style 1 third open parentheses 18 over 3 close parentheses 2 end style end fraction close parentheses to the power of negative 1 half end exponent end cell row blank equals cell open parentheses fraction numerator begin display style 1 half up diagonal strike open parentheses 6 close parentheses end strike 3 end style over denominator begin display style 1 third up diagonal strike open parentheses 6 close parentheses end strike 2 end style end fraction close parentheses to the power of negative 1 half end exponent end cell row blank equals cell open parentheses fraction numerator begin display style 3 over 2 end style over denominator begin display style 2 over 3 end style end fraction close parentheses to the power of negative 1 half end exponent end cell row blank equals cell open parentheses fraction numerator begin display style 3 end style over denominator begin display style 2 end style end fraction times 3 over 2 close parentheses to the power of negative 1 half end exponent end cell row blank equals cell open parentheses open parentheses 3 over 2 close parentheses squared close parentheses to the power of negative 1 half end exponent end cell row blank equals cell open parentheses 3 over 2 close parentheses to the power of 2 times open parentheses negative 1 half close parentheses end exponent end cell row blank equals cell open parentheses 3 over 2 close parentheses to the power of negative 1 end exponent end cell row blank equals cell fraction numerator 1 over denominator begin display style 3 over 2 end style end fraction end cell row blank equals cell 2 over 3 end cell end table$

Sehingga diperoleh $open parentheses fraction numerator begin display style 1 half open parentheses 1 half open parentheses 2 squared close parentheses 3 close parentheses 3 end style over denominator begin display style 1 third open parentheses 1 third open parentheses 3 squared close parentheses 2 close parentheses 2 end style end fraction close parentheses to the power of negative 1 half end exponent equals 2 over 3$ .

Jadi, jawaban yang benar adalah C.

Latihan Bab

Konsep Kilat

Pengertian Bilangan Berpangkat

Sifat Bilangan Berpangkat

Persamaan Bilangan Berpangkat