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Pertanyaan

Diketahui root index 6 of 7 to the power of 12 x to the power of 7 end exponent end root equals 1 over 49, maka nilai x to the power of 25 plus x to the power of 20 adalah ....space 

  1. negative 2 

  2. negative 1 

  3. 0 

  4. 1 

  5. 2 

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C. space  

Pembahasan

Diketahui root index 6 of 7 to the power of 12 x to the power of 7 end exponent end root equals 1 over 49, maka dapat diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell root index 6 of 7 to the power of 12 x to the power of 7 end exponent end root end cell equals cell 1 over 49 end cell row cell 7 to the power of fraction numerator 12 x to the power of 7 over denominator 6 end fraction end exponent end cell equals cell 1 over 7 squared end cell row cell 7 to the power of 2 x to the power of 7 end exponent end cell equals cell 7 to the power of negative 2 end exponent end cell end table

Akibatnya

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x to the power of 7 end cell equals cell negative 2 end cell row cell x to the power of 7 end cell equals cell fraction numerator negative 2 over denominator 2 end fraction end cell row cell x to the power of 7 end cell equals cell negative 1 space left right arrow x equals negative 1 end cell end table

Perhatikan bahwa, untuk x equals negative 1

table attributes columnalign right center left columnspacing 0px end attributes row cell x to the power of n end cell equals cell negative 1 comma space jika space straight n space ganjil end cell row cell x to the power of n end cell equals cell 1 comma space jika space straight n space genap end cell end table

Sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell x to the power of 25 plus x to the power of 20 end cell equals cell open parentheses negative 1 close parentheses to the power of 25 plus open parentheses negative 1 close parentheses to the power of 20 end cell row blank equals cell negative 1 plus 1 end cell row blank equals 0 end table

Jadi, jawaban yang tepat adalah C. space  

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