Pertanyaan

Bentuk sederhana dari ( x z 4 y ) − 3 ÷ ( z 2 y ) − 2 adalah....

Bentuk sederhana dari $(\frac{4 y}{x z})^{- 3} \div (\frac{2 y}{z})^{- 2}$ adalah ....

$begin mathsize 14px style fraction numerator 256 y to the power of 5 over denominator x cubed z to the power of 5 end fraction end style$
$begin mathsize 14px style fraction numerator x cubed z to the power of 5 over denominator 256 y to the power of 5 end fraction end style$
$begin mathsize 14px style fraction numerator 16 y over denominator x cubed z end fraction end style$
$begin mathsize 14px style fraction numerator x cubed z over denominator 16 y end fraction end style$

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N. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Padang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Perhatikan perhitungan berikut! Jadi, bentuk sederhana dari adalah . Dengan demikian, jawaban yang tepat adalah D.

Perhatikan perhitungan berikut!

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator 4 y over denominator x z end fraction close parentheses to the power of negative 3 end exponent divided by open parentheses fraction numerator 2 y over denominator z end fraction close parentheses to the power of negative 2 end exponent end cell equals cell fraction numerator left parenthesis 4 y right parenthesis to the power of negative 3 end exponent over denominator left parenthesis x z right parenthesis to the power of negative 3 end exponent end fraction divided by fraction numerator left parenthesis 2 y right parenthesis to the power of negative 2 end exponent over denominator z to the power of negative 2 end exponent end fraction end cell row blank equals cell fraction numerator 4 to the power of negative 3 end exponent y to the power of negative 3 end exponent over denominator x to the power of negative 3 end exponent z to the power of negative 3 end exponent end fraction divided by fraction numerator 2 to the power of negative 2 end exponent y to the power of negative 2 end exponent over denominator z to the power of negative 2 end exponent end fraction end cell row blank equals cell fraction numerator x cubed z cubed over denominator 4 cubed y cubed end fraction divided by fraction numerator z squared over denominator 2 squared y squared end fraction end cell row blank equals cell fraction numerator x cubed z cubed over denominator 64 y cubed end fraction divided by fraction numerator z squared over denominator 4 y squared end fraction end cell row blank equals cell fraction numerator x cubed z cubed over denominator 64 y cubed end fraction cross times fraction numerator 4 y squared over denominator z squared end fraction end cell row blank equals cell fraction numerator 4 x cubed z cubed y squared over denominator 64 y cubed z squared end fraction end cell row blank equals cell 1 over 16 x cubed y to the power of 2 minus 3 end exponent z to the power of 3 minus 2 end exponent end cell row blank equals cell 1 over 16 x cubed y to the power of negative 1 end exponent z to the power of 1 end cell row blank equals cell fraction numerator x cubed z over denominator 16 y end fraction end cell end table end style$

Jadi, bentuk sederhana dari $begin mathsize 14px style open parentheses fraction numerator 4 y over denominator x z end fraction close parentheses to the power of negative 3 end exponent divided by open parentheses fraction numerator 2 y over denominator z end fraction close parentheses to the power of negative 2 end exponent end style$ adalah $begin mathsize 14px style fraction numerator x cubed z over denominator 16 y end fraction end style$ .

Dengan demikian, jawaban yang tepat adalah D.