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Pertanyaan

Diketahui p equals fraction numerator 343 x to the power of a y to the power of negative b end exponent over denominator 81 x to the power of negative a plus b end exponent y to the power of b end fraction dan begin mathsize 14px style q equals fraction numerator 3 x to the power of negative a end exponent y to the power of b over denominator 49 x to the power of 2 a plus b minus 1 end exponent y to the power of negative a plus b minus 2 end exponent end fraction end style. Jika begin mathsize 14px style p q equals fraction numerator 7 y over denominator 3 cubed x to the power of 10 end fraction end style, maka hubungan yang tepat antara begin mathsize 14px style a end style dan size 14px b adalah ....

  1. begin mathsize 14px style a minus 2 b equals negative 5 end style

  2. begin mathsize 14px style a minus 2 b equals negative 12 end style

  3. begin mathsize 14px style a plus 2 b equals 8 end style

  4. begin mathsize 14px style a plus 2 b equals 11 end style

M. Haidar.

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D.

Pembahasan

Akan disederhanakan bentuk p equals fraction numerator 343 x to the power of a y to the power of negative b end exponent over denominator 81 x to the power of negative a plus b end exponent y to the power of b end fraction terlebih dahulu. Perhatikan bahwa

table attributes columnalign right center left columnspacing 0px end attributes row p equals cell fraction numerator 343 x to the power of a y to the power of negative b end exponent over denominator 81 x to the power of negative a plus b end exponent y to the power of b end fraction end cell row blank equals cell fraction numerator 7 cubed x to the power of a minus left parenthesis negative a plus b right parenthesis end exponent y to the power of negative b minus b end exponent over denominator 3 to the power of 4 end fraction end cell row blank equals cell 3 to the power of negative 4 end exponent 7 cubed x to the power of a plus a minus b end exponent y to the power of negative 2 b end exponent end cell row blank equals cell 3 to the power of negative 4 end exponent 7 cubed x to the power of 2 a minus b end exponent y to the power of negative 2 b end exponent end cell end table

Kemudian, akan disederhanakan bentuk begin mathsize 14px style q equals fraction numerator 3 x to the power of negative a end exponent y to the power of b over denominator 49 x to the power of 2 a plus b minus 1 end exponent y to the power of negative a plus b minus 2 end exponent end fraction end style. Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row q equals cell fraction numerator 3 x to the power of negative a end exponent y to the power of b over denominator 49 x to the power of 2 a plus b minus 1 end exponent y to the power of negative a plus b minus 2 end exponent end fraction end cell row blank equals cell fraction numerator 3 x to the power of negative a minus left parenthesis 2 a plus b minus 1 right parenthesis end exponent y to the power of b minus left parenthesis negative a plus b minus 2 right parenthesis end exponent over denominator 7 squared end fraction space end cell row blank equals cell 7 to the power of negative 2 end exponent 3 x to the power of negative a minus 2 a minus b plus 1 end exponent y to the power of b plus a minus b plus 2 end exponent end cell row blank equals cell 7 to the power of negative 2 end exponent 3 x to the power of negative 3 a minus b plus 1 end exponent y to the power of a plus 2 end exponent end cell end table end style

Dengan demikian, kita peroleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p q end cell equals cell open parentheses 3 to the power of negative 4 end exponent 7 cubed x to the power of 2 a minus b end exponent y to the power of negative 2 b end exponent close parentheses open parentheses 7 to the power of negative 2 end exponent 3 x to the power of negative 3 a minus b plus 1 end exponent y to the power of a plus 2 end exponent close parentheses end cell row cell fraction numerator 7 y over denominator 3 cubed x to the power of 10 end fraction end cell equals cell 3 to the power of negative 4 plus 1 end exponent 7 to the power of 3 minus 2 end exponent x to the power of 2 a minus b minus 3 a minus b plus 1 end exponent y to the power of negative 2 b plus a plus 2 end exponent end cell row cell fraction numerator 7 y over denominator 3 cubed x to the power of 10 end fraction end cell equals cell 3 to the power of negative 3 end exponent 7 x to the power of negative a minus 2 b plus 1 end exponent y to the power of a minus 2 b plus 2 end exponent end cell row cell fraction numerator 7 y over denominator 3 cubed x to the power of 10 end fraction end cell equals cell fraction numerator 7 y to the power of a minus 2 b plus 2 end exponent over denominator 3 cubed x to the power of a plus 2 b minus 1 end exponent end fraction end cell end table end style

Dari persamaan terakhir di atas, dengan menyamakan pangkat dari x dan y, kita peroleh hasil berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell x to the power of 10 end cell equals cell x to the power of a plus 2 b minus 1 end exponent end cell row 10 equals cell a plus 2 b minus 1 end cell row cell 10 plus 1 end cell equals cell a plus 2 b end cell row 11 equals cell a plus 2 b end cell row cell a plus 2 b end cell equals 11 end table

dan

table attributes columnalign right center left columnspacing 0px end attributes row cell y to the power of 1 end cell equals cell y to the power of a minus 2 b plus 2 end exponent end cell row 1 equals cell a minus 2 b plus 2 end cell row cell 1 minus 2 end cell equals cell a minus 2 b end cell row cell negative 1 end cell equals cell a minus 2 b end cell row cell a minus 2 b end cell equals cell negative 1 end cell end table

Dengan demikian, kita peroleh undefined dan begin mathsize 14px style a minus 2 b equals negative 1 end style.

Jadi, jawaban yang tepat adalah D.

103

5.0 (4 rating)

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