Pertanyaan

b. ⎝ ⎛ x − 5 1 y 2 1 ⎝ ⎛ ⎝ ⎛ x 2 1 y − 4 1 ⎠ ⎞ − 3 1 ⎠ ⎞ 12 ⎠ ⎞ 10

b. $⎝ ⎛ \frac{⎝ ⎛ ⎝ ⎛ x ^{\frac{1}{2}} y ^{- \frac{1}{4}} ⎠ ⎞ ^{- \frac{1}{3}} ⎠ ⎞ ^{12}}{x ^{- \frac{1}{5}} y ^{\frac{1}{2}}} ⎠ ⎞^{10}$

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H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

bentuk sederhana dari

bentuk sederhana dari $table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator open parentheses open parentheses x to the power of begin display style 1 half end style end exponent y to the power of negative begin display style 1 fourth end style end exponent close parentheses to the power of negative begin display style 1 third end style end exponent close parentheses to the power of 12 over denominator x to the power of negative begin display style 1 fifth end style end exponent y to the power of begin display style 1 half end style end exponent end fraction close parentheses to the power of 10 end cell equals cell y to the power of 5 over x to the power of 18 end cell end table$

Pembahasan

Bilangan berpangkat bulat positif dapat didefinisikan sebagai berikut. Ingat sifat bilangan berpangkat berikut. sehingga penyelesaian soal di atas, yaitu Dengan demikian, bentuk sederhana dari

Bilangan berpangkat bulat positif dapat didefinisikan sebagai berikut.

a to the power of n equals stack a cross times a cross times a cross times horizontal ellipsis cross times a with underbrace below table row blank cell space space space space space space space space end cell cell n space text faktor end text end cell end table

Ingat sifat bilangan berpangkat berikut.

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

open parentheses a to the power of m close parentheses to the power of n equals a to the power of m n end exponent

open parentheses a b close parentheses to the power of m equals a to the power of m b to the power of m

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 comma space b not equal to 0

a to the power of negative m end exponent equals 1 over a to the power of m comma space a not equal to 0

sehingga penyelesaian soal di atas, yaitu

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator open parentheses open parentheses x to the power of begin display style 1 half end style end exponent y to the power of negative begin display style 1 fourth end style end exponent close parentheses to the power of negative begin display style 1 third end style end exponent close parentheses to the power of 12 over denominator x to the power of negative begin display style 1 fifth end style end exponent y to the power of begin display style 1 half end style end exponent end fraction close parentheses to the power of 10 end cell equals cell open parentheses fraction numerator open parentheses open parentheses x to the power of begin display style 1 half end style end exponent close parentheses to the power of negative begin display style 1 third end style end exponent open parentheses y to the power of negative begin display style 1 fourth end style end exponent close parentheses to the power of negative begin display style 1 third end style end exponent close parentheses to the power of 12 over denominator x to the power of negative 1 fifth end exponent y to the power of 1 half end exponent end fraction close parentheses to the power of 10 end cell row blank equals cell open parentheses fraction numerator open parentheses x to the power of negative begin display style 1 over 6 end style end exponent y to the power of begin display style 1 over 12 end style end exponent close parentheses to the power of 12 over denominator x to the power of negative 1 fifth end exponent y to the power of 1 half end exponent end fraction close parentheses to the power of 10 end cell row blank equals cell open parentheses fraction numerator open parentheses x to the power of negative 1 over 6 end exponent close parentheses to the power of 12 open parentheses y to the power of 1 over 12 end exponent close parentheses to the power of 12 over denominator x to the power of negative 1 fifth end exponent y to the power of 1 half end exponent end fraction close parentheses to the power of 10 end cell row blank equals cell open parentheses fraction numerator x to the power of negative 2 end exponent y over denominator x to the power of negative 1 fifth end exponent y to the power of 1 half end exponent end fraction close parentheses to the power of 10 end cell row blank equals cell open parentheses x to the power of negative 2 end exponent y close parentheses to the power of 10 over open parentheses x to the power of negative 1 fifth end exponent y to the power of 1 half end exponent close parentheses to the power of 10 end cell row blank equals cell fraction numerator open parentheses x to the power of negative 2 end exponent close parentheses to the power of 10 open parentheses y close parentheses to the power of 10 over denominator open parentheses x to the power of negative 1 fifth end exponent close parentheses to the power of 10 open parentheses y to the power of 1 half end exponent close parentheses to the power of 10 end fraction end cell row blank equals cell fraction numerator x to the power of negative 20 end exponent y to the power of 10 over denominator x to the power of negative 2 end exponent y to the power of 5 end fraction end cell row blank equals cell x to the power of negative 20 minus open parentheses negative 2 close parentheses end exponent y to the power of 10 minus 5 end exponent end cell row blank equals cell x to the power of negative 18 end exponent y to the power of 5 end cell row blank equals cell y to the power of 5 over x to the power of 18 end cell end table$

Dengan demikian, bentuk sederhana dari $table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses fraction numerator open parentheses open parentheses x to the power of begin display style 1 half end style end exponent y to the power of negative begin display style 1 fourth end style end exponent close parentheses to the power of negative begin display style 1 third end style end exponent close parentheses to the power of 12 over denominator x to the power of negative begin display style 1 fifth end style end exponent y to the power of begin display style 1 half end style end exponent end fraction close parentheses to the power of 10 end cell equals cell y to the power of 5 over x to the power of 18 end cell end table$