Pertanyaan

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

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

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

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.

dimana a not equal to 0 .

Berdasarkan sifat-sifat di atas, maka:

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

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 $open parentheses a plus b close parentheses to the power of negative 3 over 4 end exponent cross times open parentheses a plus b close parentheses to the power of 1 over 8 end exponent divided by open parentheses a plus b close parentheses to the power of 1 half end exponent equals fraction numerator 1 over denominator root index 8 of left parenthesis a plus b right parenthesis to the power of 9 end root end fraction$ .