Pertanyaan

Diketahui nilai x = 16 1 , y = 8 1 , dan z = 4 1 . Hasil dari x 5 y − 1 z 2 x 3 y 2 adalah ...

Diketahui nilai $x = \frac{1}{16}$ , $y = \frac{1}{8}$ , dan $z = \frac{1}{4}$ . Hasil dari $\frac{x ^{3} y ^{2}}{x ^{5} y ^{- 1} z ^{2}}$ adalah ...

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Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Diketahui nilai , , dan , ingat sifat bilangan berpangkat: maka kemudian substitusikan nilai , , dan : Oleh karena itu, jawaban yang benar adalah B.

Diketahui nilai x equals 1 over 16 , y equals 1 over 8 , dan z equals 1 fourth , ingat sifat bilangan berpangkat:

maka

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

kemudian substitusikan nilai x equals 1 over 16 , y equals 1 over 8 , dan z equals 1 fourth :

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator y cubed over denominator x squared z squared end fraction end cell equals cell fraction numerator open parentheses begin display style 1 over 8 end style close parentheses cubed over denominator open parentheses begin display style 1 over 16 end style close parentheses squared open parentheses begin display style 1 fourth end style close parentheses squared end fraction end cell row blank equals cell fraction numerator open parentheses begin display style 1 over 2 cubed end style close parentheses cubed over denominator open parentheses begin display style 1 over 2 to the power of 4 end style close parentheses squared open parentheses begin display style 1 over 2 squared end style close parentheses squared end fraction end cell row blank equals cell fraction numerator open parentheses 2 to the power of negative 3 end exponent close parentheses cubed over denominator open parentheses 2 to the power of negative 4 end exponent close parentheses squared open parentheses 2 to the power of negative 2 end exponent close parentheses squared end fraction end cell row blank equals cell fraction numerator 2 to the power of negative 9 end exponent over denominator 2 to the power of negative 8 end exponent times 2 to the power of negative 4 end exponent end fraction end cell row blank equals cell 2 to the power of negative 9 end exponent over 2 to the power of negative 12 end exponent end cell row blank equals cell 2 to the power of negative 9 minus left parenthesis negative 12 right parenthesis end exponent end cell row blank equals cell 2 to the power of negative 9 plus 12 end exponent end cell row blank equals cell 2 cubed end cell row blank equals 8 end table$

Oleh karena itu, jawaban yang benar adalah B.