Pertanyaan

Jika 5 10 x = 1600 dan , nilai 8 − y ( 5 x − 1 ) 5 adalah ....

Jika $5^{10 x} = 1600$ dan $2^\sqrt y=25$ , nilai $\frac{( 5 ^{x - 1} ) ^{5}}{8 ^{- y}}$ adalah ....

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Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Ingat kembali sifat-sifat bilangan berpangkat berikut. sehingga dapat ditentukan nilaidari bentuk berikut. Jadi, jawaban yang benar adalah D.

Ingat kembali sifat-sifat bilangan berpangkat berikut.

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.