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A. Khairunisa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

Perhatikan bahwa Jadi, hasil dari adalah . Dengan demikian, jawaban yang tepat adalah D.

Perhatikan bahwa

$begin mathsize 12px style 3 cube root of cube root of square root of 72 a to the power of 4 b to the power of 49 end root end root end root divided by 9 root index 6 of open parentheses 81 a to the power of negative 54 end exponent b to the power of 32 close parentheses to the power of 1 over 6 end exponent end root equals fraction numerator 3 cube root of cube root of square root of 72 a to the power of 4 b to the power of 49 end root end root end root over denominator 9 root index 6 of open parentheses 81 a to the power of negative 54 end exponent b to the power of 32 close parentheses to the power of 1 over 6 end exponent end root end fraction equals fraction numerator cube root of cube root of open parentheses 72 a to the power of 4 b to the power of 49 close parentheses to the power of 1 half end exponent end root end root over denominator 3 root index 6 of open parentheses 9 squared open parentheses a to the power of negative 27 end exponent close parentheses squared open parentheses b to the power of 16 close parentheses squared close parentheses to the power of 1 over 6 end exponent end root end fraction equals fraction numerator cube root of open parentheses open parentheses 72 a to the power of 4 b to the power of 49 close parentheses to the power of 1 half end exponent close parentheses to the power of 1 third end exponent end root over denominator 3 root index 6 of open parentheses open parentheses 9 a to the power of negative 27 end exponent b to the power of 16 close parentheses squared close parentheses to the power of 1 over 6 end exponent end root end fraction equals fraction numerator cube root of open parentheses 72 a to the power of 4 b to the power of 49 close parentheses to the power of 1 over 6 end exponent end root over denominator 3 root index 6 of open parentheses 9 a to the power of negative 27 end exponent b to the power of 16 close parentheses to the power of 1 third end exponent end root end fraction equals fraction numerator open parentheses open parentheses 72 a to the power of 4 b to the power of 49 close parentheses to the power of 1 over 6 end exponent close parentheses to the power of 1 third end exponent over denominator 3 open parentheses open parentheses 9 a to the power of negative 27 end exponent b to the power of 16 close parentheses to the power of 1 third end exponent close parentheses to the power of 1 over 6 end exponent end fraction equals fraction numerator open parentheses 72 a to the power of 4 b to the power of 49 close parentheses to the power of 1 over 18 end exponent over denominator 3 open parentheses 9 a to the power of negative 27 end exponent b to the power of 16 close parentheses to the power of 1 over 18 end exponent end fraction equals fraction numerator root index 18 of 72 a to the power of 4 b to the power of 49 end root over denominator 3 root index 18 of 9 a to the power of negative 27 end exponent b to the power of 16 end root end fraction equals 1 third root index 18 of fraction numerator 72 a to the power of 4 b to the power of 49 over denominator 9 a to the power of negative 27 end exponent b to the power of 16 end fraction end root equals 1 third root index 18 of 8 a to the power of 4 minus open parentheses negative 27 close parentheses end exponent b to the power of 49 minus 16 end exponent end root equals 1 third root index 18 of 8 a to the power of 31 b to the power of 33 end root equals 1 third open parentheses 8 a to the power of 31 b to the power of 33 close parentheses to the power of 1 over 18 end exponent equals 1 third open parentheses 8 to the power of 1 over 18 end exponent a to the power of 1 13 over 18 end exponent b to the power of 1 15 over 18 end exponent close parentheses equals 1 third a b open parentheses 8 a to the power of 13 b to the power of 15 close parentheses to the power of 1 over 18 end exponent equals 1 third a b root index 18 of 8 a to the power of 13 b to the power of 15 end root end style$

Jadi, hasil dari adalah .

Dengan demikian, jawaban yang tepat adalah D.