Pertanyaan

Jika , maka nilai p + q + r adalah ....

Jika $begin mathsize 14px style fraction numerator square root of root index 6 of open parentheses 114 x to the power of negative 18 end exponent y to the power of 12 close parentheses to the power of 1 half end exponent end root end root over denominator cube root of square root of open parentheses 19 x to the power of 28 y to the power of negative 13 end exponent close parentheses to the power of 1 fourth end exponent end root end root end fraction equals 6 to the power of p x to the power of q y to the power of r end style$ , maka nilai $p + q + r$ adalah ....

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A. Khairunisa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

Perhatikan bahwa Karena , maka didapat , , dan . Jadi, Dengan demikian, jawaban yang tepat adalah C.

Perhatikan bahwa

$begin mathsize 12px style fraction numerator square root of root index 6 of open parentheses 114 x to the power of negative 18 end exponent y to the power of 12 close parentheses to the power of 1 half end exponent end root end root over denominator cube root of square root of open parentheses 19 x to the power of 28 y to the power of negative 13 end exponent close parentheses to the power of 1 fourth end exponent end root end root end fraction equals fraction numerator square root of open parentheses open parentheses 114 x to the power of negative 18 end exponent y to the power of 12 close parentheses to the power of 1 half end exponent close parentheses to the power of 1 over 6 end exponent end root over denominator cube root of open parentheses open parentheses 19 x to the power of 28 y to the power of negative 13 end exponent close parentheses to the power of 1 fourth end exponent close parentheses to the power of 1 half end exponent end root end fraction equals fraction numerator square root of open parentheses 114 x to the power of negative 18 end exponent y to the power of 12 close parentheses to the power of 1 over 12 end exponent end root over denominator cube root of open parentheses 19 x to the power of 28 y to the power of negative 13 end exponent close parentheses to the power of 1 over 8 end exponent end root end fraction equals open parentheses open parentheses 114 x to the power of negative 18 end exponent y to the power of 12 close parentheses to the power of 1 over 12 end exponent close parentheses to the power of 1 half end exponent over open parentheses open parentheses 19 x to the power of 28 y to the power of negative 13 end exponent close parentheses to the power of 1 over 8 end exponent close parentheses to the power of 1 third end exponent equals open parentheses 114 x to the power of negative 18 end exponent y to the power of 12 close parentheses to the power of 1 over 24 end exponent over open parentheses 19 x to the power of 28 y to the power of negative 13 end exponent close parentheses to the power of 1 over 24 end exponent equals fraction numerator root index 24 of 114 x to the power of negative 18 end exponent y to the power of 12 end root over denominator root index 24 of 19 x to the power of 28 y to the power of negative 13 end exponent end root end fraction equals root index 24 of 6 x to the power of negative 18 minus 28 end exponent y to the power of 12 minus open parentheses negative 13 close parentheses end exponent end root equals root index 24 of 6 x to the power of negative 46 end exponent y to the power of 25 end root equals open parentheses 6 x to the power of negative 46 end exponent y to the power of 25 close parentheses to the power of 1 over 24 end exponent equals 6 to the power of 1 over 24 end exponent x to the power of negative 46 over 24 end exponent y to the power of 25 over 24 end exponent end style$

Karena undefined , maka didapat , , dan .

Jadi,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p plus q plus r end cell equals cell 1 over 24 minus 46 over 24 plus 25 over 24 end cell row blank equals cell negative 20 over 24 end cell row blank equals cell negative 5 over 6 end cell end table end style

Dengan demikian, jawaban yang tepat adalah C.