Pertanyaan

( 3 4 2 3 ) 4 ⋅ 6 2 ÷ ( 2 3 ⋅ 3 6 ) − 2 =...

$(\frac{2 ^{3}}{3 ^{4}})^{4} \cdot 6^{2} \div (2^{3} \cdot 3^{6})^{- 2}$ =...

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Jawaban terverifikasi

Jawaban

jawaban yang benar adalah E.

Pembahasan

Ingat kembali bahwa akar adalah kebalikan dari kuadrat (atau pangkat dua) maka akar dapat ditulis dengan pangkat . Sehingga, diperoleh perhitungan berikut ini. Dengan demikian, hasil dari adalah . Oleh karena itu, jawaban yang benar adalah E.

Ingat kembali bahwa akar adalah kebalikan dari kuadrat (atau pangkat dua) maka akar dapat ditulis dengan pangkat 1 half .

$table attributes columnalign right center left columnspacing 0px end attributes row cell square root of a end cell equals cell a to the power of bevelled 1 half end exponent end cell row cell a to the power of negative bevelled 1 half end exponent end cell equals cell 1 over a to the power of begin display style bevelled 1 half end style end exponent equals fraction numerator 1 over denominator square root of a end fraction end cell row cell square root of a to the power of n end root end cell equals cell open parentheses a to the power of n close parentheses to the power of bevelled 1 half end exponent end cell end table$

Sehingga, diperoleh perhitungan berikut ini.

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses square root of 2 cubed over 3 to the power of 4 end root close parentheses to the power of 4 times 6 squared divided by open parentheses square root of 2 cubed times 3 to the power of 6 end root close parentheses to the power of negative 2 end exponent end cell equals cell open parentheses fraction numerator square root of 2 cubed end root over denominator square root of 3 to the power of 4 end root end fraction close parentheses to the power of 4 times 6 squared divided by open parentheses square root of 2 cubed times 3 to the power of 6 end root close parentheses to the power of negative 2 end exponent end cell row blank equals cell open parentheses 2 to the power of begin display style 3 over 2 end style end exponent over 3 to the power of begin display style 4 over 2 end style end exponent close parentheses to the power of 4 times 6 squared divided by open parentheses open parentheses 2 cubed.3 to the power of 6 close parentheses to the power of 1 half end exponent close parentheses to the power of negative 2 end exponent end cell row blank equals cell open parentheses 2 to the power of begin display style 3 over 2 end style end exponent close parentheses to the power of 4 over open parentheses 3 to the power of 4 over 2 end exponent close parentheses to the power of 4 times open parentheses 2.3 close parentheses squared divided by open parentheses 2 cubed.3 to the power of 6 close parentheses to the power of negative 1 end exponent end cell row blank equals cell 2 to the power of 6 over 3 to the power of 8. open parentheses 2 squared.3 squared close parentheses divided by open parentheses 2 to the power of negative 3 end exponent.3 to the power of negative 6 end exponent close parentheses end cell row blank equals cell fraction numerator 2 to the power of 6 times 2 squared times 3 squared over denominator 3 to the power of 8 end fraction divided by fraction numerator 2 to the power of negative 3 end exponent.3 to the power of negative 6 end exponent over denominator 1 end fraction end cell row blank equals cell fraction numerator 2 to the power of 6 times 2 squared times 3 squared over denominator 3 to the power of 8 end fraction cross times fraction numerator 1 over denominator 2 to the power of negative 3 end exponent.3 to the power of negative 6 end exponent end fraction end cell row blank equals cell 2 to the power of 6 plus 2 minus left parenthesis negative 3 right parenthesis end exponent.3 to the power of 2 minus 8 minus left parenthesis negative 6 right parenthesis end exponent end cell row blank equals cell 2 to the power of 11.3 to the power of 0 end cell row blank equals cell 2 to the power of 11.1 end cell row blank equals cell 2 to the power of 11 end cell end table$

Dengan demikian, hasil dari open parentheses square root of 2 cubed over 3 to the power of 4 end root close parentheses to the power of 4 times 6 squared divided by open parentheses square root of 2 cubed times 3 to the power of 6 end root close parentheses to the power of negative 2 end exponent adalah 2 to the power of 11 .

Oleh karena itu, jawaban yang benar adalah E.