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Bentuk sederhana (20x−1y5z25x3y−3z4​)−21​ adalah ...

Pertanyaan

Bentuk sederhana open parentheses fraction numerator 5 x cubed y to the power of negative 3 end exponent z to the power of 4 over denominator 20 x to the power of negative 1 end exponent y to the power of 5 z squared end fraction close parentheses to the power of negative 1 half end exponent adalah ...

  1. fraction numerator y to the power of 4 over denominator 2 x squared z cubed end fraction 

  2. fraction numerator y to the power of 4 over denominator 2 x squared z end fraction 

  3. fraction numerator 2 y to the power of 4 over denominator x squared z end fraction 

  4. fraction numerator 2 x squared over denominator y to the power of 4 z cubed end fraction 

  5. fraction numerator 2 y to the power of 4 over denominator x squared z cubed end fraction  

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Pembahasan:

Ingat sifat bilangan berpangkat:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses x y close parentheses to the power of n end cell equals cell x to the power of n y to the power of n end cell row cell open parentheses x to the power of m close parentheses to the power of n end cell equals cell x to the power of m n end exponent end cell row cell x to the power of m over x to the power of n end cell equals cell x to the power of m minus n end exponent end cell row cell x to the power of negative m end exponent end cell equals cell 1 over x to the power of m end cell end table    

maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 5 x cubed y to the power of negative 3 end exponent z to the power of 4 over denominator 20 x to the power of negative 1 end exponent y to the power of 5 z squared end fraction close parentheses to the power of negative 1 half end exponent end cell equals cell open parentheses 5 over 20 times x cubed over x to the power of negative 1 end exponent times y to the power of negative 3 end exponent over y to the power of 5 times z to the power of 4 over z squared close parentheses to the power of negative 1 half end exponent end cell row blank equals cell open parentheses 5 over 20 close parentheses to the power of negative 1 half end exponent times open parentheses x cubed over x to the power of negative 1 end exponent close parentheses to the power of negative 1 half end exponent times open parentheses y to the power of negative 3 end exponent over y to the power of 5 close parentheses to the power of negative 1 half end exponent times open parentheses z to the power of 4 over z squared close parentheses to the power of negative 1 half end exponent end cell row blank equals cell open parentheses 1 fourth close parentheses to the power of negative 1 half end exponent times open parentheses x to the power of negative begin display style 3 over 2 end style end exponent over x to the power of begin display style 1 half end style end exponent close parentheses times open parentheses y to the power of begin display style 3 over 2 end style end exponent over y to the power of negative begin display style 5 over 2 end style end exponent close parentheses times open parentheses z to the power of negative begin display style 4 over 2 end style end exponent over z to the power of negative begin display style 2 over 2 end style end exponent close parentheses end cell row blank equals cell open parentheses 1 over 2 squared close parentheses to the power of negative 1 half end exponent times open parentheses x to the power of negative begin display style 3 over 2 end style end exponent over x to the power of begin display style 1 half end style end exponent close parentheses times open parentheses y to the power of begin display style 3 over 2 end style end exponent over y to the power of negative begin display style 5 over 2 end style end exponent close parentheses times open parentheses z to the power of negative begin display style 4 over 2 end style end exponent over z to the power of negative begin display style 2 over 2 end style end exponent close parentheses end cell row blank equals cell 2 to the power of negative 2 open parentheses negative 1 half close parentheses end exponent times x to the power of 4 open parentheses negative 1 half close parentheses end exponent times y to the power of negative 8 open parentheses negative 1 half close parentheses end exponent times z to the power of 2 open parentheses negative 1 half close parentheses end exponent end cell row blank equals cell 2 to the power of 1 times x to the power of negative 2 end exponent times y to the power of 4 times z to the power of negative 1 end exponent end cell row blank equals cell 2 times 1 over x squared times y to the power of 4 times 1 over z end cell row blank equals cell fraction numerator 2 y to the power of 4 over denominator x squared z end fraction end cell end table   

Bentuk sederhana open parentheses fraction numerator 5 x cubed y to the power of negative 3 end exponent z to the power of 4 over denominator 20 x to the power of negative 1 end exponent y to the power of 5 z squared end fraction close parentheses to the power of negative 1 half end exponent adalah fraction numerator 2 y to the power of 4 over denominator x squared z end fraction.

Oleh karena itu, jawaban yang benar adalah C. 

Jawaban terverifikasi

Dijawab oleh:

N. Puspita

Terakhir diupdate 07 Oktober 2021

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