Pertanyaan

Bentuk sederhana dari ⎝ ⎛ x 3 1 y 3 2 z 3 1 x 3 2 y 3 4 z − 3 1 ⎠ ⎞ 6 adalah ...

Bentuk sederhana dari $⎝ ⎛ \frac{x ^{\frac{2}{3}} y ^{\frac{4}{3}} z ^{- \frac{1}{3}}}{x ^{\frac{1}{3}} y ^{\frac{2}{3}} z ^{\frac{1}{3}}} ⎠ ⎞^{6}$ adalah ...

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Pembahasan

Bentuk sederhanya adalah sebagai berikut: Maka, bentuk sederhana dari adalah .

Bentuk sederhanya adalah sebagai berikut:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator x to the power of begin display style 2 over 3 end style end exponent y to the power of begin display style 4 over 3 end style end exponent z to the power of negative begin display style 1 third end style end exponent over denominator x to the power of begin display style 1 third end style end exponent y to the power of begin display style 2 over 3 end style end exponent z to the power of begin display style 1 third end style end exponent end fraction close parentheses to the power of 6 end cell equals cell open parentheses fraction numerator x to the power of begin display style fraction numerator 2 cross times 6 over denominator 3 end fraction end style end exponent y to the power of begin display style fraction numerator 4 cross times 6 over denominator 3 end fraction end style end exponent z to the power of negative begin display style fraction numerator 1 cross times 6 over denominator 3 end fraction end style end exponent over denominator x to the power of begin display style fraction numerator 1 cross times 6 over denominator 3 end fraction end style end exponent y to the power of begin display style fraction numerator 2 cross times 6 over denominator 3 end fraction end style end exponent z to the power of begin display style fraction numerator 1 cross times 6 over denominator 3 end fraction end style end exponent end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator x to the power of begin display style 12 over 3 end style end exponent y to the power of begin display style 24 over 3 end style end exponent z to the power of negative begin display style 6 over 3 end style end exponent over denominator x to the power of begin display style 6 over 3 end style end exponent y to the power of begin display style 12 over 3 end style end exponent z to the power of begin display style 6 over 3 end style end exponent end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator x to the power of 4 y to the power of 8 z to the power of negative 2 end exponent over denominator x squared y to the power of 4 z squared end fraction close parentheses end cell row blank equals cell x to the power of 4 minus 2 end exponent y to the power of 8 minus 4 end exponent z to the power of negative 2 minus 2 end exponent end cell row blank equals cell x squared y to the power of 4 z to the power of negative 4 end exponent end cell end table$

Maka, bentuk sederhana dari $open parentheses fraction numerator x to the power of begin display style 2 over 3 end style end exponent y to the power of begin display style 4 over 3 end style end exponent z to the power of negative begin display style 1 third end style end exponent over denominator x to the power of begin display style 1 third end style end exponent y to the power of begin display style 2 over 3 end style end exponent z to the power of begin display style 1 third end style end exponent end fraction close parentheses to the power of 6$ adalah x squared y to the power of 4 z to the power of negative 4 end exponent .