Roboguru

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Pertanyaan

16 to the power of 2 over 3 end exponent cross times 16 to the power of 5 over 6 end exponent space colon space 16 to the power of 3 over 4 end exponent equals space horizontal ellipsis.space 

  1. 2 

  2. 4 

  3. 8 

  4. 16 

Pembahasan Soal:

Ingat kembali pengertian dan sifat bilangan berpangkat:

  • table row cell a to the power of m end cell equals cell stack a cross times a cross times midline horizontal ellipsis cross times a with underbrace below end cell row blank blank cell blank presuperscript text sebanyak end text space m end presuperscript end cell end table
  • bentuk a to the power of m dengan m bilangan genap, akan menghasilkan bilangan genap
  • a to the power of m cross times a to the power of n equals a to the power of m plus n end exponent 
  • a to the power of m divided by a to the power of n equals a to the power of m minus n end exponent dengan a not equal to 0 

Dengan demikian, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 16 to the power of 2 over 3 end exponent cross times 16 to the power of 5 over 6 end exponent divided by 16 to the power of 3 over 4 end exponent end cell row blank equals cell 16 to the power of 2 over 3 plus 5 over 6 end exponent divided by 16 to the power of 3 over 4 end exponent end cell row blank equals cell 16 to the power of 2 over 3 plus 5 over 6 minus 3 over 4 end exponent end cell row blank equals cell 16 to the power of fraction numerator 2 cross times 4 over denominator 3 cross times 4 end fraction plus fraction numerator 5 cross times 2 over denominator 6 cross times 2 end fraction minus fraction numerator 3 cross times 3 over denominator 4 cross times 3 end fraction end exponent end cell row blank equals cell 16 to the power of 8 over 12 plus 10 over 12 minus 9 over 12 end exponent end cell row blank equals cell 16 to the power of fraction numerator 8 plus 10 minus 9 over denominator 12 end fraction end exponent end cell row blank equals cell 16 to the power of 9 over 12 end exponent end cell row blank equals cell open parentheses 2 to the power of 4 close parentheses to the power of 9 over 12 end exponent end cell row blank equals cell open parentheses 2 close parentheses to the power of 4 cross times 9 over 12 end exponent end cell row blank equals cell open parentheses 2 close parentheses to the power of 36 over 12 end exponent end cell row blank equals cell open parentheses 2 close parentheses cubed end cell row blank equals cell 2 cross times 2 cross times 2 end cell row blank equals 8 end table   

Jadi, 16 to the power of 2 over 3 end exponent cross times 16 to the power of 5 over 6 end exponent space colon space 16 to the power of 3 over 4 end exponent equals 8.

Oleh karena itu, jawaban yang benar adalah C.space 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Juli 2021

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