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Sederhanakan pemangkatan bilangan-bilangan berikut! 3. ⎝ ⎛ ​ y 2 2 1 ​ x − 3 2 ​ ​ ⎠ ⎞ ​ − 4

Sederhanakan pemangkatan bilangan-bilangan berikut!

3.

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D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

bentuk sederhana dari adalah .

bentuk sederhana dari open parentheses x to the power of negative begin display style 2 over 3 end style end exponent over y to the power of 2 begin display style 1 half end style end exponent close parentheses to the power of negative 4 end exponent adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x squared space cube root of x squared end root y to the power of 10 end cell end table.

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Pembahasan

Sebelum menjawab soal, ingatlah sifat-sifat bilangan berpangkat pecahan berikut. Berdasarkan sifat-sifat di atas, maka: Dengan demikian, bentuk sederhana dari adalah .

Sebelum menjawab soal, ingatlah sifat-sifat bilangan berpangkat pecahan berikut.

left parenthesis straight i 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 left parenthesis ii right parenthesis space open parentheses a to the power of m over n end exponent close parentheses to the power of p equals a to the power of m over n cross times p 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 open parentheses a to the power of begin display style m over n end style end exponent over b to the power of begin display style r over s end style end exponent close parentheses to the power of p equals open parentheses a to the power of begin display style m over n end style end exponent close parentheses to the power of p over open parentheses b to the power of begin display style r over s end style end exponent close parentheses to the power of p

Berdasarkan sifat-sifat di atas, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses x to the power of negative begin display style 2 over 3 end style end exponent over y to the power of 2 begin display style 1 half end style end exponent close parentheses to the power of negative 4 end exponent end cell equals cell open parentheses x to the power of negative 2 over 3 end exponent close parentheses to the power of negative 4 end exponent over open parentheses y to the power of 2 1 half end exponent close parentheses to the power of negative 4 end exponent end cell row blank equals cell x to the power of negative begin display style 2 over 3 end style cross times open parentheses negative 4 close parentheses end exponent over y to the power of 2 begin display style 1 half end style cross times open parentheses negative 4 close parentheses end exponent end cell row blank equals cell x to the power of begin display style 8 over 3 end style end exponent over y to the power of negative 10 end exponent end cell row blank equals cell fraction numerator x to the power of begin display style 8 over 3 end style end exponent over denominator begin display style 1 over y to the power of 10 end style end fraction end cell row blank equals cell x to the power of 2 2 over 3 end exponent y to the power of 10 end cell row blank equals cell x squared space cube root of x squared end root y to the power of 10 end cell end table

Dengan demikian, bentuk sederhana dari open parentheses x to the power of negative begin display style 2 over 3 end style end exponent over y to the power of 2 begin display style 1 half end style end exponent close parentheses to the power of negative 4 end exponent adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x squared space cube root of x squared end root y to the power of 10 end cell end table.

Latihan Bab

Konsep Kilat

Pengertian Bilangan Berpangkat

Sifat Bilangan Berpangkat

Persamaan Bilangan Berpangkat

23

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