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Pertanyaan

Sederhanakan operasi bilangan berpangkat berikut! a. ( a 4 3 ​ × a − 8 3 ​ ÷ a 6 1 ​ ) 8 b. ( a 2 1 ​ × a − 3 2 ​ ÷ b 6 1 ​ ) − 6

Sederhanakan operasi bilangan berpangkat berikut!

a.
b.

8 dari 10 siswa nilainya naik

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D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

bentuk sederhana dari , dan .

bentuk sederhana dari  open parentheses a to the power of 3 over 4 end exponent cross times a to the power of negative 3 over 8 end exponent divided by a to the power of 1 over 6 end exponent close parentheses to the power of 8 equals a to the power of 5 over 3 end exponent, dan open parentheses a to the power of 1 half end exponent cross times a to the power of negative 2 over 3 end exponent divided by b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent equals a b.

Pembahasan

Ingatlah sifat-sifat bilangan berpangkat berikut. Berdasarkan sifat-sifat di atas, maka: a) b) Dengan demikian, bentuk sederhana dari , dan .

Ingatlah sifat-sifat bilangan berpangkat berikut.

left parenthesis straight i right parenthesis space a to the power of m cross times a to the power of n equals a to the power of m plus n end exponent left parenthesis ii right parenthesis space a to the power of m divided by a to the power of n equals a to the power of m minus n end exponent left parenthesis iii right parenthesis space open parentheses a divided by b close parentheses to the power of m equals a to the power of m divided by b to the power of m left parenthesis iv right parenthesis space open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent  

Berdasarkan sifat-sifat di atas, maka:

a)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a to the power of 3 over 4 end exponent cross times a to the power of negative 3 over 8 end exponent divided by a to the power of 1 over 6 end exponent close parentheses to the power of 8 end cell equals cell open parentheses a to the power of 3 over 4 plus open parentheses negative 3 over 8 close parentheses minus 1 over 6 end exponent close parentheses to the power of 8 end cell row blank equals cell open parentheses a to the power of fraction numerator 18 minus 9 minus 4 over denominator 24 end fraction end exponent close parentheses to the power of 8 end cell row blank equals cell open parentheses a to the power of 5 over 24 end exponent close parentheses to the power of 8 end cell row blank equals cell a to the power of 5 over 24 cross times 8 end exponent end cell row blank equals cell a to the power of 40 over 24 end exponent end cell row blank equals cell a to the power of 5 over 3 end exponent end cell end table

b)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a to the power of 1 half end exponent cross times a to the power of negative 2 over 3 end exponent divided by b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent end cell equals cell open parentheses a to the power of 1 half plus open parentheses negative 2 over 3 close parentheses end exponent divided by b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent end cell row blank equals cell open parentheses a to the power of fraction numerator 3 minus 4 over denominator 6 end fraction end exponent divided by b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent end cell row blank equals cell open parentheses a to the power of negative 1 over 6 end exponent divided by b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent end cell row blank equals cell open parentheses a to the power of negative 1 over 6 end exponent close parentheses to the power of negative 6 end exponent divided by open parentheses b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent end cell row blank equals cell a to the power of negative fraction numerator 1 over denominator up diagonal strike 6 end fraction cross times open parentheses negative up diagonal strike 6 close parentheses end exponent divided by b to the power of fraction numerator 1 over denominator up diagonal strike 6 end fraction cross times open parentheses negative up diagonal strike 6 close parentheses end exponent end cell row blank equals cell a divided by b to the power of negative 1 end exponent end cell row blank equals cell a divided by 1 over b end cell row blank equals cell a b end cell end table

Dengan demikian, bentuk sederhana dari  open parentheses a to the power of 3 over 4 end exponent cross times a to the power of negative 3 over 8 end exponent divided by a to the power of 1 over 6 end exponent close parentheses to the power of 8 equals a to the power of 5 over 3 end exponent, dan open parentheses a to the power of 1 half end exponent cross times a to the power of negative 2 over 3 end exponent divided by b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent equals a b.

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