Pertanyaan

Nilai dari ( 9 4 ) 2 1 + ( 27 8 ) 3 1 + ( 81 16 ) 4 1 = ...

Nilai dari $(\frac{4}{9})^{\frac{1}{2}} + (\frac{8}{27})^{\frac{1}{3}} + (\frac{16}{81})^{\frac{1}{4}} = ...$

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Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

diperoleh hasilnya yaitu .

diperoleh hasilnya yaitu

Pembahasan

Diperhatikan Ingat sifat eksponen Diperoleh perhitungan Dengan demikian, diperoleh hasilnya yaitu .

Diperhatikan

open parentheses 4 over 9 close parentheses to the power of 1 half end exponent plus open parentheses 8 over 27 close parentheses to the power of 1 third end exponent plus open parentheses 16 over 81 close parentheses to the power of 1 fourth end exponent

Ingat sifat eksponen

open parentheses a over b close parentheses to the power of m equals a to the power of m over b to the power of m a to the power of 1 over n end exponent equals n-th root of a

Diperoleh perhitungan

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 4 over 9 close parentheses to the power of 1 half end exponent plus open parentheses 8 over 27 close parentheses to the power of 1 third end exponent plus open parentheses 16 over 81 close parentheses to the power of 1 fourth end exponent end cell row blank equals cell 4 to the power of begin display style 1 half end style end exponent over 9 to the power of begin display style 1 half end style end exponent plus 8 to the power of begin display style 1 third end style end exponent over 27 to the power of begin display style 1 third end style end exponent plus 16 to the power of begin display style 1 fourth end style end exponent over 81 to the power of begin display style 1 fourth end style end exponent end cell row blank equals cell fraction numerator square root of 4 over denominator cube root of 9 end fraction plus fraction numerator cube root of 8 over denominator cube root of 27 end fraction plus fraction numerator fourth root of 16 over denominator fourth root of 81 end fraction end cell row blank equals cell 2 over 3 plus 2 over 3 plus 2 over 3 end cell row blank equals cell 6 over 3 end cell row blank equals 2 end table$

Dengan demikian, diperoleh hasilnya yaitu .