Pertanyaan

Bentuk sederhana dari ( x 4 y − 5 z 2 x 3 y − 1 z − 4 ) 2 adalah …

Bentuk sederhana dari $(\frac{x ^{3} y ^{- 1} z ^{- 4}}{x ^{4} y ^{- 5} z ^{2}})^{2}$ adalah $\dots$

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

bentuk sederhana dari adalah

bentuk sederhana dari $open parentheses fraction numerator x cubed y to the power of negative 1 end exponent z to the power of negative 4 end exponent over denominator x to the power of 4 y to the power of negative 5 end exponent z squared end fraction close parentheses squared$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator y to the power of 8 over denominator x squared z to the power of 12 end fraction end cell end table.$

Pembahasan

Ingat kembali bahwa: Dengan menggunakan sifat di atas, maka bentuk sederhana dari adalah Dengan demikian,bentuk sederhana dari adalah

Ingat kembali bahwa:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a over b close parentheses to the power of m end cell equals cell a to the power of m over b to the power of m end cell 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 end table

Dengan menggunakan sifat di atas, maka bentuk sederhana dari $open parentheses fraction numerator x cubed y to the power of negative 1 end exponent z to the power of negative 4 end exponent over denominator x to the power of 4 y to the power of negative 5 end exponent z squared end fraction close parentheses squared$ adalah

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator x cubed y to the power of negative 1 end exponent z to the power of negative 4 end exponent over denominator x to the power of 4 y to the power of negative 5 end exponent z squared end fraction close parentheses squared end cell equals cell open parentheses x cubed y to the power of negative 1 end exponent z to the power of negative 4 end exponent close parentheses squared over open parentheses x to the power of 4 y to the power of negative 5 end exponent z squared close parentheses squared end cell row blank equals cell fraction numerator x to the power of 6 y to the power of negative 2 end exponent z to the power of negative 8 end exponent over denominator x to the power of 8 y to the power of negative 10 end exponent z to the power of 4 end fraction end cell row blank equals cell x to the power of 6 times x to the power of negative 8 end exponent times y to the power of negative 2 end exponent times y to the power of negative open parentheses negative 10 close parentheses end exponent times z to the power of negative 8 end exponent times z to the power of negative 4 end exponent end cell row blank equals cell x to the power of 6 minus 8 end exponent times y to the power of negative 2 plus 10 end exponent times z to the power of negative 8 minus 4 end exponent end cell row blank equals cell x to the power of negative 2 end exponent times y to the power of 8 times z to the power of negative 12 end exponent end cell row cell open parentheses fraction numerator x cubed y to the power of negative 1 end exponent z to the power of negative 4 end exponent over denominator x to the power of 4 y to the power of negative 5 end exponent z squared end fraction close parentheses squared end cell equals cell fraction numerator y to the power of 8 over denominator x squared z to the power of 12 end fraction end cell end table$

Dengan demikian, bentuk sederhana dari $open parentheses fraction numerator x cubed y to the power of negative 1 end exponent z to the power of negative 4 end exponent over denominator x to the power of 4 y to the power of negative 5 end exponent z squared end fraction close parentheses squared$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator y to the power of 8 over denominator x squared z to the power of 12 end fraction end cell end table.$