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Diantara bilangan berikut mana yang paling besar?

Diantara bilangan berikut mana yang paling besar?

  1. begin mathsize 14px style open parentheses 3 to the power of 4 close parentheses to the power of 13 end style 

  2. begin mathsize 14px style open parentheses open parentheses 3 to the power of 30 close parentheses to the power of 12 close parentheses to the power of 1 over 20 end exponent end style 

  3. begin mathsize 14px style 3 to the power of 30 plus 3 to the power of 30 plus 3 to the power of 30 end style 

  4. begin mathsize 14px style 4 times 3 to the power of 51 end style 

  5. begin mathsize 14px style 4 times 300 to the power of 1 half end exponent end style 

Jawaban:

Dengan menggunakan sifat perpangkatan, maka didapatkan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 3 to the power of 4 close parentheses to the power of 13 end cell equals cell 3 to the power of 4 cross times 13 end exponent end cell row blank equals cell 3 to the power of 42 end cell row blank blank blank row cell open parentheses open parentheses 3 to the power of 30 close parentheses to the power of 12 close parentheses to the power of 1 over 20 end exponent end cell equals cell 3 to the power of 30 cross times 12 cross times 1 over 20 end exponent end cell row blank equals cell 3 to the power of 18 end cell row blank blank blank row cell 3 to the power of 30 plus 3 to the power of 30 plus 3 to the power of 30 end cell equals cell 3 cross times open parentheses 3 cross times 10 close parentheses to the power of 30 end cell row blank equals cell 3 cross times 3 to the power of 30 cross times 10 to the power of 30 end cell row blank equals cell 10 to the power of 30 cross times 3 to the power of 31 end cell row blank blank blank row cell 4 times 3 to the power of 51 end cell equals cell 4 cross times 3 to the power of 51 end cell row blank blank blank row cell 4 times 300 to the power of 1 half end exponent end cell equals cell 4 cross times open parentheses 3 cross times 10 close parentheses to the power of 1 half end exponent end cell row blank equals cell 4 cross times square root of 10 cross times square root of 3 end cell end table end style

Jadi, jawaban yang tepat adalah C.

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