Pertanyaan

Jika diketahui a = 64 , b = 128 dan c = 27 , maka nilai dari 4 1 a b 7 1 27 a 3 1 b 7 2 c − 3 2 adalah...

Jika diketahui $a = 64, b = 128 dan c = 27$ , maka nilai dari $\frac{27 a ^{\frac{1}{3}} b ^{\frac{2}{7}} c ^{- \frac{2}{3}}}{\frac{1}{4} a b ^{\frac{1}{7}}}$ adalah...

R. Febrianti

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

nilai dari adalah .

nilai dari $fraction numerator 27 a to the power of 1 third end exponent b to the power of 2 over 7 end exponent c to the power of negative begin display style 2 over 3 end style end exponent over denominator 1 fourth a b to the power of begin display style 1 over 7 end style end exponent end fraction$ adalah 3 over 2

Pembahasan

Berdasarkan sifat bilangan berpangkat a m ÷ a n = a m − n maka 4 1 a b 7 1 27 a 3 1 b 7 2 c − 3 2 = = = = 4 1 27 a 3 1 − 1 b 7 2 − 7 1 c − 3 2 ( 27 ÷ 4 1 ) ( a 3 1 − 3 3 b 7 2 − 7 1 c − 3 2 ) ( 27 × 4 ) ( a − 3 2 b 7 1 c − 3 2 ) 108 a − 3 2 b 7 1 c − 3 2 Berdasarkan sifat bilangan berpangkat a − m = a m 1 maka 4 1 a b 7 1 27 a 3 1 b 7 2 c − 3 2 = = = = = 4 1 27 a 3 1 − 1 b 7 2 − 7 1 c − 3 2 ( 27 ÷ 4 1 ) ( a 3 1 − 3 3 b 7 2 − 7 1 c − 3 2 ) ( 27 × 4 ) ( a − 3 2 b 7 1 c − 3 2 ) 108 a − 3 2 b 7 1 c − 3 2 a 3 2 c 3 2 108 b 7 1 Diketahui a = 64 , b = 128 dan c = 27 maka 4 1 a b 7 1 27 a 3 1 b 7 2 c − 3 2 = = = = = = = 4 1 27 a 3 1 − 1 b 7 2 − 7 1 c − 3 2 ( 27 ÷ 4 1 ) ( a 3 1 − 3 3 b 7 2 − 7 1 c − 3 2 ) ( 27 × 4 ) ( a − 3 2 b 7 1 c − 3 2 ) 108 a − 3 2 b 7 1 c − 3 2 a 3 2 c 3 2 108 b 7 1 ( 64 ) 3 2 ( 27 ) 3 2 108 ( 128 ) 7 1 ( 4 3 ) 3 2 ( 3 3 ) 3 2 108 ( 2 7 ) 7 1 Berdasarkan sifat bilangan berpangkat ( a m ) n = a m × n maka 4 1 a b 7 1 27 a 3 1 b 7 2 c − 3 2 = = = = = = = = = = = 4 1 27 a 3 1 − 1 b 7 2 − 7 1 c − 3 2 ( 27 ÷ 4 1 ) ( a 3 1 − 3 3 b 7 2 − 7 1 c − 3 2 ) ( 27 × 4 ) ( a − 3 2 b 7 1 c − 3 2 ) 108 a − 3 2 b 7 1 c − 3 2 a 3 2 c 3 2 108 b 7 1 ( 64 ) 3 2 ( 27 ) 3 2 108 ( 128 ) 7 1 ( 4 3 ) 3 2 ( 3 3 ) 3 2 108 ( 2 7 ) 7 1 4 3 × 3 2 3 3 × 3 2 108 × 2 7 × 7 1 4 1 × 3 1 108 × 2 1 4 × 3 108 × 2 2 3 Dengan demikian, nilai dari adalah .

Berdasarkan sifat bilangan berpangkat $a^{m} \div a^{n} = a^{m - n}$ maka

$\frac{27 a ^{\frac{1}{3}} b ^{\frac{2}{7}} c ^{- \frac{2}{3}}}{\frac{1}{4} a b ^{\frac{1}{7}}} = = = = \frac{27}{\frac{1}{4}} a^{\frac{1}{3} - 1} b^{\frac{2}{7} - \frac{1}{7}} c^{- \frac{2}{3}} (27 \div \frac{1}{4}) (a^{\frac{1}{3} - \frac{3}{3}} b^{\frac{2}{7} - \frac{1}{7}} c^{- \frac{2}{3}}) (27 \times 4) (a^{- \frac{2}{3}} b^{\frac{1}{7}} c^{- \frac{2}{3}}) 108 a^{- \frac{2}{3}} b^{\frac{1}{7}} c^{- \frac{2}{3}}$

Berdasarkan sifat bilangan berpangkat $a^{- m} = \frac{1}{a ^{m}}$ maka

$\frac{27 a ^{\frac{1}{3}} b ^{\frac{2}{7}} c ^{- \frac{2}{3}}}{\frac{1}{4} a b ^{\frac{1}{7}}} = = = = = \frac{27}{\frac{1}{4}} a^{\frac{1}{3} - 1} b^{\frac{2}{7} - \frac{1}{7}} c^{- \frac{2}{3}} (27 \div \frac{1}{4}) (a^{\frac{1}{3} - \frac{3}{3}} b^{\frac{2}{7} - \frac{1}{7}} c^{- \frac{2}{3}}) (27 \times 4) (a^{- \frac{2}{3}} b^{\frac{1}{7}} c^{- \frac{2}{3}}) 108 a^{- \frac{2}{3}} b^{\frac{1}{7}} c^{- \frac{2}{3}} \frac{108 b ^{\frac{1}{7}}}{a ^{\frac{2}{3}} c ^{\frac{2}{3}}}$

Diketahui $a = 64, b = 128 dan c = 27$ maka

$\frac{27 a ^{\frac{1}{3}} b ^{\frac{2}{7}} c ^{- \frac{2}{3}}}{\frac{1}{4} a b ^{\frac{1}{7}}} = = = = = = = \frac{27}{\frac{1}{4}} a^{\frac{1}{3} - 1} b^{\frac{2}{7} - \frac{1}{7}} c^{- \frac{2}{3}} (27 \div \frac{1}{4}) (a^{\frac{1}{3} - \frac{3}{3}} b^{\frac{2}{7} - \frac{1}{7}} c^{- \frac{2}{3}}) (27 \times 4) (a^{- \frac{2}{3}} b^{\frac{1}{7}} c^{- \frac{2}{3}}) 108 a^{- \frac{2}{3}} b^{\frac{1}{7}} c^{- \frac{2}{3}} \frac{108 b ^{\frac{1}{7}}}{a ^{\frac{2}{3}} c ^{\frac{2}{3}}} \frac{108 ( 128 ) ^{\frac{1}{7}}}{( 64 ) ^{\frac{2}{3}} ( 27 ) ^{\frac{2}{3}}} \frac{108 ( 2 ^{7} ) ^{\frac{1}{7}}}{( 4 ^{3} ) ^{\frac{2}{3}} ( 3 ^{3} ) ^{\frac{2}{3}}}$

Berdasarkan sifat bilangan berpangkat $(a^{m})^{n} = a^{m \times n}$ maka

$\frac{27 a ^{\frac{1}{3}} b ^{\frac{2}{7}} c ^{- \frac{2}{3}}}{\frac{1}{4} a b ^{\frac{1}{7}}} = = = = = = = = = = = \frac{27}{\frac{1}{4}} a^{\frac{1}{3} - 1} b^{\frac{2}{7} - \frac{1}{7}} c^{- \frac{2}{3}} (27 \div \frac{1}{4}) (a^{\frac{1}{3} - \frac{3}{3}} b^{\frac{2}{7} - \frac{1}{7}} c^{- \frac{2}{3}}) (27 \times 4) (a^{- \frac{2}{3}} b^{\frac{1}{7}} c^{- \frac{2}{3}}) 108 a^{- \frac{2}{3}} b^{\frac{1}{7}} c^{- \frac{2}{3}} \frac{108 b ^{\frac{1}{7}}}{a ^{\frac{2}{3}} c ^{\frac{2}{3}}} \frac{108 ( 128 ) ^{\frac{1}{7}}}{( 64 ) ^{\frac{2}{3}} ( 27 ) ^{\frac{2}{3}}} \frac{108 ( 2 ^{7} ) ^{\frac{1}{7}}}{( 4 ^{3} ) ^{\frac{2}{3}} ( 3 ^{3} ) ^{\frac{2}{3}}} \frac{108 \times 2 ^{7 \times \frac{1}{7}}}{4 ^{3 \times \frac{2}{3}} 3 ^{3 \times \frac{2}{3}}} \frac{108 \times 2 ^{1}}{4 ^{1} \times 3 ^{1}} \frac{108 \times 2}{4 \times 3} \frac{3}{2}$

Dengan demikian, nilai dari $fraction numerator 27 a to the power of 1 third end exponent b to the power of 2 over 7 end exponent c to the power of negative begin display style 2 over 3 end style end exponent over denominator 1 fourth a b to the power of begin display style 1 over 7 end style end exponent end fraction$ adalah 3 over 2 .