Pertanyaan

Bentuk sederhana dari ( 24 x 5 y − 3 z 3 x − 2 y z − 3 ) − 1 adalah ....

Bentuk sederhana dari $(\frac{3 x ^{- 2} y z ^{- 3}}{24 x ^{5} y ^{- 3} z})^{- 1}$ adalah ....

P. Afrisno

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

diperoleh .

diperoleh $open parentheses fraction numerator 3 x to the power of negative 2 end exponent y z to the power of negative 3 end exponent over denominator 24 x to the power of 5 y to the power of negative 3 end exponent z end fraction close parentheses to the power of negative 1 end exponent equals fraction numerator 8 x to the power of 7 z to the power of 4 over denominator y to the power of 4 end fraction$ .

Pembahasan

Ingat kembali sifat-sifat bilangan berpangkat berikut. sehingga dapat ditentukan bentuk sederhana dari bentuk berikut. Dengan demikian diperoleh .

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 end table

sehingga dapat ditentukan bentuk sederhana dari bentuk berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 3 x to the power of negative 2 end exponent y z to the power of negative 3 end exponent over denominator 24 x to the power of 5 y to the power of negative 3 end exponent z end fraction close parentheses to the power of negative 1 end exponent end cell equals cell open parentheses 3 over 24 x to the power of negative 2 minus 5 end exponent y to the power of 1 minus open parentheses negative 3 close parentheses end exponent z to the power of negative 3 minus 1 end exponent close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses 1 over 8 x to the power of negative 7 end exponent y to the power of 1 plus 3 end exponent z to the power of negative 4 end exponent close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses 1 over 8 times 1 over x to the power of 7 times y to the power of 4 times 1 over z to the power of 4 close parentheses to the power of negative 1 end exponent end cell row blank equals cell open parentheses fraction numerator y to the power of 4 over denominator 8 x to the power of 7 z to the power of 4 end fraction close parentheses to the power of negative 1 end exponent end cell row blank equals cell fraction numerator 1 over denominator begin display style fraction numerator y to the power of 4 over denominator 8 x to the power of 7 z to the power of 4 end fraction end style end fraction end cell row blank equals cell fraction numerator 8 x to the power of 7 z to the power of 4 over denominator y to the power of 4 end fraction end cell end table$

Dengan demikian diperoleh $open parentheses fraction numerator 3 x to the power of negative 2 end exponent y z to the power of negative 3 end exponent over denominator 24 x to the power of 5 y to the power of negative 3 end exponent z end fraction close parentheses to the power of negative 1 end exponent equals fraction numerator 8 x to the power of 7 z to the power of 4 over denominator y to the power of 4 end fraction$ .