Pertanyaan

Sederhanakan operasi bilangan berpangkat berikut ! c. 3 a 4 3 × 2 a − 8 3 × ( b 2 1 ÷ b − 4 3 ) d. x − 4 5 × x − 8 5 × ( y 4 3 ÷ y − 2 1 )

Sederhanakan operasi bilangan berpangkat berikut !

c. $3 a^{\frac{3}{4}} \times 2 a^{- \frac{3}{8}} \times (b^{\frac{1}{2}} \div b^{- \frac{3}{4}})$
d. $x^{- \frac{5}{4}} \times x^{- \frac{5}{8}} \times (y^{\frac{3}{4}} \div y^{- \frac{1}{2}})$

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Klaim

D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

hasil dari , dan .

hasil dari

3 a to the power of 3 over 4 end exponent cross times 2 a to the power of negative 3 over 8 end exponent cross times open parentheses b to the power of 1 half end exponent divided by b to the power of negative 3 over 4 end exponent close parentheses equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank b end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell root index 8 of a cubed end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fourth root of b end cell end table

, dan $x to the power of negative 5 over 4 end exponent space cross times space x to the power of negative 5 over 8 end exponent space cross times space open parentheses space y to the power of 3 over 4 end exponent divided by y to the power of negative 1 half end exponent close parentheses equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator y space fourth root of y over denominator x space root index 8 of x to the power of 7 end root end fraction end cell end table$ .

Pembahasan

Ingatlah sifat-sifat bilangan berpangkat berikut. Berdasarkan sifat-sifat di atas, maka: c) d) Dengan demikian, hasil dari , dan .

Ingatlah sifat-sifat bilangan berpangkat berikut.

Berdasarkan sifat-sifat di atas, maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell 3 a to the power of 3 over 4 end exponent cross times 2 a to the power of negative 3 over 8 end exponent cross times open parentheses b to the power of 1 half end exponent divided by b to the power of negative 3 over 4 end exponent close parentheses end cell equals cell 6 a to the power of 3 over 4 plus open parentheses negative 3 over 8 close parentheses end exponent cross times open parentheses b to the power of 1 half minus open parentheses negative 3 over 4 close parentheses end exponent close parentheses end cell row blank equals cell 6 a to the power of fraction numerator 6 minus 3 over denominator 8 end fraction end exponent cross times open parentheses b to the power of fraction numerator 2 plus 3 over denominator 4 end fraction end exponent close parentheses end cell row blank equals cell 6 a to the power of 3 over 8 end exponent cross times b to the power of 5 over 4 end exponent end cell row blank equals cell 6 space root index 8 of a cubed end root cross times b cross times b to the power of 1 fourth end exponent end cell row blank equals cell 6 b space root index 8 of a cubed end root space fourth root of b end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell x to the power of negative 5 over 4 end exponent space cross times space x to the power of negative 5 over 8 end exponent space cross times space open parentheses space y to the power of 3 over 4 end exponent divided by y to the power of negative 1 half end exponent close parentheses end cell equals cell x to the power of negative 5 over 4 plus open parentheses negative 5 over 8 close parentheses end exponent cross times open parentheses y to the power of 3 over 4 minus open parentheses negative 1 half close parentheses end exponent close parentheses end cell row blank equals cell x to the power of fraction numerator negative 10 minus 5 over denominator 8 end fraction end exponent space cross times space y to the power of fraction numerator 3 plus 2 over denominator 4 end fraction end exponent space end cell row blank equals cell x to the power of negative 15 over 8 end exponent space cross times space y to the power of 5 over 4 end exponent end cell row blank equals cell y to the power of begin display style 5 over 4 end style end exponent over x to the power of begin display style 15 over 8 end style end exponent end cell row blank equals cell fraction numerator y times y to the power of begin display style 1 fourth end style end exponent over denominator x times x to the power of begin display style 7 over 8 end style end exponent end fraction end cell row blank equals cell fraction numerator y space fourth root of y over denominator x space root index 8 of x to the power of 7 end root end fraction end cell end table$

Dengan demikian, hasil dari , dan $x to the power of negative 5 over 4 end exponent space cross times space x to the power of negative 5 over 8 end exponent space cross times space open parentheses space y to the power of 3 over 4 end exponent divided by y to the power of negative 1 half end exponent close parentheses equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator y space fourth root of y over denominator x space root index 8 of x to the power of 7 end root end fraction end cell end table$ .