Pertanyaan

( 125 x − 1 y 2 8 x 2 y − 4 ) 3 2 = ....

$(\frac{8 x ^{2} y ^{- 4}}{125 x ^{- 1} y ^{2}})^{\frac{2}{3}} = ....$

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Habis dalam

Klaim

P. Afrisno

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah A.

Pembahasan

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

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 a to the power of p over a to the power of q end cell equals cell a to the power of p minus q end exponent end cell 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 end table

Sehingga dapat ditentukan hasil dari bentuk berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 8 x squared y to the power of negative 4 end exponent over denominator 125 x to the power of negative 1 end exponent y squared end fraction close parentheses to the power of 2 over 3 end exponent end cell equals cell open parentheses 8 over 125 x to the power of 2 minus open parentheses negative 1 close parentheses end exponent y to the power of negative 4 minus 2 end exponent close parentheses to the power of 2 over 3 end exponent end cell row blank equals cell open parentheses 2 cubed over 5 cubed x to the power of 2 plus 1 end exponent y to the power of negative 6 end exponent close parentheses to the power of 2 over 3 end exponent end cell row blank equals cell open parentheses open parentheses 2 over 5 close parentheses cubed x cubed y to the power of negative 6 end exponent close parentheses to the power of 2 over 3 end exponent end cell row blank equals cell open parentheses 2 over 5 close parentheses to the power of 3 times 2 over 3 end exponent x to the power of 3 times 2 over 3 end exponent y to the power of negative 6 times 2 over 3 end exponent end cell row blank equals cell open parentheses 0 comma 4 close parentheses squared x squared y to the power of negative 4 end exponent end cell row blank equals cell 0 comma 16 x squared y to the power of negative 4 end exponent end cell end table$

Sehingga diperoleh $open parentheses fraction numerator 8 x squared y to the power of negative 4 end exponent over denominator 125 x to the power of negative 1 end exponent y squared end fraction close parentheses to the power of 2 over 3 end exponent equals 0 comma 16 x squared y to the power of negative 4 end exponent$ .

Jadi, jawaban yang benar adalah A.