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(91−x3x+2​​)32​=....

Pertanyaan

open parentheses square root of 3 to the power of x plus 2 end exponent over 9 to the power of 1 minus x end exponent end root close parentheses to the power of 2 over 3 end exponent equals.... 

  1. 3 

  2. 3 to the power of x 

  3. 3 to the power of x plus 1 end exponent 

  4. 3 to the power of 2 x plus 1 end exponent 

  5. 3 to the power of 2 x plus 2 end exponent 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Jika diberikan bilangan riil a space dan space bb not equal to 0 dan bilangan rasional p comma space q comma space r maka berlaku sifat berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell a to the power of p over q end exponent end cell equals cell q-th root of a to the power of p end root end cell row cell b to the power of p over b to the power of q end cell equals cell b 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 row cell open parentheses a to the power of p over b to the power of p close parentheses to the power of r end cell equals cell a to the power of p r end exponent over b to the power of q r 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 square root of 3 to the power of x plus 2 end exponent over 9 to the power of 1 minus x end exponent end root close parentheses to the power of 2 over 3 end exponent end cell equals cell open parentheses open parentheses 3 to the power of x plus 2 end exponent over 9 to the power of 1 minus x end exponent close parentheses to the power of 1 half end exponent close parentheses to the power of 2 over 3 end exponent end cell row blank equals cell 3 to the power of open parentheses x plus 2 close parentheses times begin display style 1 half end style times begin display style 2 over 3 end style end exponent over open parentheses 3 squared close parentheses to the power of open parentheses 1 minus x close parentheses times begin display style 1 half end style times begin display style 2 over 3 end style end exponent end cell row blank equals cell 3 to the power of begin display style fraction numerator x plus 2 over denominator 3 end fraction end style end exponent over 3 to the power of 2 times begin display style fraction numerator 1 minus x over denominator 3 end fraction end style end exponent end cell row blank equals cell 3 to the power of begin display style fraction numerator x plus 2 over denominator 3 end fraction end style end exponent over 3 to the power of begin display style fraction numerator 2 minus 2 x over denominator 3 end fraction end style end exponent end cell row blank equals cell 3 to the power of fraction numerator x plus 2 over denominator 3 end fraction minus fraction numerator 2 minus 2 x over denominator 3 end fraction end exponent end cell row blank equals cell 3 to the power of fraction numerator x plus 2 minus 2 plus 2 x over denominator 3 end fraction end exponent end cell row blank equals cell 3 to the power of fraction numerator 3 x over denominator 3 end fraction end exponent end cell row blank equals cell 3 to the power of x end cell end table  

Sehingga diperoleh open parentheses square root of 3 to the power of x plus 2 end exponent over 9 to the power of 1 minus x end exponent end root close parentheses to the power of 2 over 3 end exponent equals 3 to the power of x.

Jadi, jawaban yang benar adalah B.

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