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Sederhanakan operasi hitung berikut! a. a x − y × a x + y ÷ a 2 x b. ( a + b ) − 4 3 ​ × ( a + b ) 8 1 ​ ÷ ( a + b ) 2 1 ​

Sederhanakan operasi hitung berikut!

a.
b.

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D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

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Jawaban

hasil dari , dan .

hasil dari  a to the power of x minus y end exponent cross times a to the power of x plus y end exponent divided by a to the power of 2 x end exponent equals 1, dan open parentheses a plus b close parentheses to the power of negative 3 over 4 end exponent cross times open parentheses a plus b close parentheses to the power of 1 over 8 end exponent divided by open parentheses a plus b close parentheses to the power of 1 half end exponent equals fraction numerator 1 over denominator root index 8 of left parenthesis a plus b right parenthesis to the power of 9 end root end fraction .

Pembahasan

Ingatlah sifat-sifat bilangan berpangkat berikut. dimana . Berdasarkan sifat-sifat di atas, maka: a) b) Dengan demikian, hasil 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 a to the power of negative m end exponent equals 1 over a to the power of m left parenthesis iv right parenthesis space a to the power of 0 equals 1 left parenthesis straight v right parenthesis space a to the power of m over n end exponent equals n-th root of a to the power of m end root 

dimana a not equal to 0.

Berdasarkan sifat-sifat di atas, maka:

a)

table attributes columnalign right center left columnspacing 0px end attributes row cell a to the power of x minus y end exponent cross times a to the power of x plus y end exponent divided by a to the power of 2 x end exponent end cell equals cell a to the power of left parenthesis x minus y right parenthesis plus left parenthesis x plus y right parenthesis end exponent divided by a to the power of 2 x end exponent end cell row blank equals cell a to the power of 2 x end exponent divided by a to the power of 2 x end exponent end cell row blank equals cell a to the power of 2 x minus 2 x end exponent end cell row blank equals cell a to the power of 0 end cell row blank equals 1 end table 

b)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a plus b close parentheses to the power of negative 3 over 4 end exponent cross times open parentheses a plus b close parentheses to the power of 1 over 8 end exponent divided by open parentheses a plus b close parentheses to the power of 1 half end exponent end cell equals cell open parentheses a plus b close parentheses to the power of negative 3 over 4 plus 1 over 8 end exponent divided by open parentheses a plus b close parentheses to the power of 1 half end exponent end cell row blank equals cell open parentheses a plus b close parentheses to the power of fraction numerator negative 6 plus 1 over denominator 8 end fraction end exponent divided by open parentheses a plus b close parentheses to the power of 1 half end exponent end cell row blank equals cell open parentheses a plus b close parentheses to the power of negative 5 over 8 end exponent divided by open parentheses a plus b close parentheses to the power of 1 half end exponent end cell row blank equals cell open parentheses a plus b close parentheses to the power of negative 5 over 8 minus 1 half end exponent end cell row blank equals cell open parentheses a plus b close parentheses to the power of fraction numerator negative 5 minus 4 over denominator 8 end fraction end exponent end cell row blank equals cell open parentheses a plus b close parentheses to the power of negative 9 over 8 end exponent end cell row blank equals cell 1 over open parentheses a plus b close parentheses to the power of begin display style 9 over 8 end style end exponent end cell row blank equals cell fraction numerator 1 over denominator root index 8 of left parenthesis a plus b right parenthesis to the power of 9 end root end fraction end cell end table 

Dengan demikian, hasil dari  a to the power of x minus y end exponent cross times a to the power of x plus y end exponent divided by a to the power of 2 x end exponent equals 1, dan open parentheses a plus b close parentheses to the power of negative 3 over 4 end exponent cross times open parentheses a plus b close parentheses to the power of 1 over 8 end exponent divided by open parentheses a plus b close parentheses to the power of 1 half end exponent equals fraction numerator 1 over denominator root index 8 of left parenthesis a plus b right parenthesis to the power of 9 end root end fraction .

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