Pertanyaan

Sederhanakalanlah dan hitunglah 8 ⋅ 3 − 5 ⋅ 12 5 − 1 2 4 ⋅ 9 − 2 ⋅ 5 − 3 .

Sederhanakalanlah dan hitunglah $\frac{2 ^{4} \cdot 9 ^{- 2} \cdot 5 ^{- 3}}{8 \cdot 3 ^{- 5} \cdot 12 5 ^{- 1}}$ .

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Jawaban terverifikasi

Jawaban

hasil dari adalah 6.

hasil dari $begin mathsize 14px style fraction numerator 2 to the power of 4 times 9 to the power of negative 2 end exponent times 5 to the power of negative 3 end exponent over denominator 8 times 3 to the power of negative 5 end exponent times 125 to the power of negative 1 end exponent end fraction end style$ adalah 6.

Pembahasan

Dengan menggunakan sifat eksponen a m a n = a n − m dan ( a n ) m = a nm , maka didapatkan: Jadi, hasil dari adalah 6.

Dengan menggunakan sifat eksponen $\frac{a ^{n}}{a ^{m}} = a^{n - m} dan (a^{n})^{m} = a^{nm}$ , maka didapatkan:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 to the power of 4 times 9 to the power of negative 2 end exponent times 5 to the power of negative 3 end exponent over denominator 8 times 3 to the power of negative 5 end exponent times 125 to the power of negative 1 end exponent end fraction end cell equals cell fraction numerator 2 to the power of 4 times left parenthesis 3 squared right parenthesis to the power of negative 2 end exponent times 5 to the power of negative 3 end exponent over denominator 2 cubed times 3 to the power of negative 5 end exponent times left parenthesis 5 cubed right parenthesis to the power of negative 1 end exponent end fraction end cell row blank equals cell fraction numerator 2 to the power of 4 times 3 to the power of negative 4 end exponent times 5 to the power of negative 3 end exponent over denominator 2 cubed times 3 to the power of negative 5 end exponent times 5 to the power of negative 3 end exponent end fraction end cell row blank equals cell 2 to the power of 4 minus 3 end exponent times 3 to the power of negative 4 minus left parenthesis negative 5 right parenthesis end exponent times 5 to the power of negative 3 minus left parenthesis negative 3 right parenthesis end exponent end cell row blank equals cell 2 to the power of 1 times 3 to the power of 1 times 5 to the power of 0 end cell row blank equals 6 end table end style$

Jadi, hasil dari $begin mathsize 14px style fraction numerator 2 to the power of 4 times 9 to the power of negative 2 end exponent times 5 to the power of negative 3 end exponent over denominator 8 times 3 to the power of negative 5 end exponent times 125 to the power of negative 1 end exponent end fraction end style$ adalah 6.