Roboguru

Jika  dan , nilai  adalah ....

Pertanyaan

Jika 5 to the power of 10 x end exponent equals 1600 dan 2 to the power of square root of y end exponent equals 25, nilai open parentheses 5 to the power of x minus 1 end exponent close parentheses to the power of 5 over 8 to the power of negative square root of y end exponent adalah ....

  1. 50 

  2. 100 

  3. 150 

  4. 200 

  5. 250 

Pembahasan Soal:

Ingat kembali sifat-sifat bilangan berpangkat berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell a to the power of negative m end exponent end cell equals cell 1 over a to the power of m end cell row cell a to the power of m over a to the power of n end cell equals cell a to the power of m minus n end exponent comma space dengan space a not equal to 0 end cell row cell open parentheses a to the power of m close parentheses to the power of n end cell equals cell a to the power of m n end exponent end cell end table  

sehingga dapat ditentukan nilai dari bentuk berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 5 to the power of x minus 1 end exponent close parentheses to the power of 5 over 8 to the power of negative square root of y end exponent end cell equals cell 5 to the power of 5 x minus 5 end exponent over open parentheses 2 cubed close parentheses to the power of negative square root of y end exponent end cell row blank equals cell fraction numerator begin display style 5 to the power of 5 x end exponent over 5 to the power of 5 end style over denominator begin display style 1 over open parentheses 2 cubed close parentheses to the power of square root of y end exponent end style end fraction end cell row blank equals cell fraction numerator 5 to the power of 5 x end exponent times 2 to the power of 3 square root of y end exponent over denominator 5 to the power of 5 end fraction end cell row blank equals cell fraction numerator 5 to the power of begin display style fraction numerator 10 x over denominator 2 end fraction end style end exponent times open parentheses 2 to the power of square root of y end exponent close parentheses cubed over denominator 5 to the power of 5 end fraction end cell row blank equals cell fraction numerator open parentheses 5 to the power of 10 x end exponent close parentheses to the power of begin display style 1 half end style end exponent times open parentheses 2 to the power of square root of y end exponent close parentheses cubed over denominator 3125 end fraction end cell row blank equals cell fraction numerator open parentheses 1600 close parentheses to the power of begin display style 1 half end style end exponent times open parentheses 25 close parentheses cubed over denominator 3125 end fraction end cell row blank equals cell fraction numerator open parentheses 40 squared close parentheses to the power of begin display style 1 half end style end exponent times 15625 over denominator 3125 end fraction end cell row blank equals cell 40 times 5 end cell row blank equals 200 end table   

Jadi, jawaban yang benar adalah D.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 26 Juli 2021

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