Pertanyaan

Hitunglah: 2 7 3 2 − 6 , 2 7 − 3 1 + 3 1 6 4 3 + 8 , 1 6 − 2 1 − 5

Hitunglah: $\frac{1 6 ^{\frac{3}{4}} + 8 , 1 6 ^{- \frac{1}{2}} - 5}{2 7 ^{\frac{2}{3}} - 6 , 2 7 ^{- \frac{1}{3}} + 3}$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

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$begin mathsize 14px style fraction numerator 16 to the power of 3 over 4 end exponent plus 8.16 to the power of negative 1 half end exponent minus 5 over denominator 27 to the power of 2 over 3 end exponent minus 6.27 to the power of negative 1 third end exponent plus 3 end fraction equals 0.29238 end style$ .

Pembahasan

Diketahui: Sifat bilangan berpangkat yang digunakan: Sehingga didapat: Jadi, .

Diketahui:

$begin mathsize 14px style fraction numerator 16 to the power of begin display style 3 over 4 end style end exponent plus 8 comma 16 to the power of negative begin display style 1 half end style end exponent minus 5 over denominator 27 to the power of begin display style 2 over 3 end style end exponent minus 6 comma 27 to the power of negative begin display style 1 third end style end exponent plus 3 end fraction end style$

Sifat bilangan berpangkat yang digunakan:
1. space open parentheses a to the power of m close parentheses to the power of n equals a to the power of m n end exponent 2. space a to the power of negative m end exponent equals 1 over a to the power of m

Sehingga didapat:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 16 to the power of 3 over 4 end exponent plus 8 comma 16 to the power of negative 1 half end exponent minus 5 over denominator 27 to the power of 2 over 3 end exponent minus 6 comma 27 to the power of negative 1 third end exponent plus 3 end fraction end cell equals cell fraction numerator open parentheses 2 to the power of 4 close parentheses to the power of begin display style 3 over 4 end style end exponent plus 8 comma 16 to the power of negative 1 half end exponent minus 5 over denominator open parentheses 3 cubed close parentheses to the power of begin display style 2 over 3 end style end exponent minus 6 comma 27 to the power of negative 1 third end exponent plus 3 end fraction end cell row blank equals cell fraction numerator 2 cubed plus 8 comma 16 to the power of negative 1 half end exponent minus 5 over denominator 3 squared minus 6 comma 27 to the power of negative 1 third end exponent plus 3 end fraction end cell row blank equals cell fraction numerator 8 plus 8 comma 16 to the power of negative 1 half end exponent minus 5 over denominator 9 minus 6 comma 27 to the power of negative 1 third end exponent plus 3 end fraction end cell row blank equals cell fraction numerator 3 plus fraction numerator 1 over denominator 8 comma 16 to the power of 1 half end exponent end fraction over denominator 12 minus fraction numerator 1 over denominator 6 comma 27 to the power of 1 third end exponent end fraction end fraction end cell row blank equals cell fraction numerator 3 plus begin display style fraction numerator 1 over denominator 2 comma 85657 end fraction end style over denominator 12 minus begin display style fraction numerator 1 over denominator 1 comma 84397 end fraction end style end fraction end cell row blank equals cell fraction numerator 3 plus 0 comma 35007 over denominator 12 minus 0 comma 5423 end fraction end cell row blank equals cell fraction numerator 3 comma 35007 over denominator 11 comma 45769 end fraction end cell row blank equals cell 0 comma 29238 end cell end table$

Jadi, $begin mathsize 14px style fraction numerator 16 to the power of 3 over 4 end exponent plus 8.16 to the power of negative 1 half end exponent minus 5 over denominator 27 to the power of 2 over 3 end exponent minus 6.27 to the power of negative 1 third end exponent plus 3 end fraction equals 0.29238 end style$ .