Pertanyaan

Nyatakan dalam bilangan berpangkat ! h. 4 16 y 6 3 x 2 i. 3 − 64 x − 6 x − 5 j. 4 81 x − 5 y 6 3 x − 8

Nyatakan dalam bilangan berpangkat !

h. $\frac{3 x ^{2}}{4 16 y ^{6}}$

i. $\frac{x ^{- 5}}{3 - 64 x ^{- 6}}$

j. $\frac{3 x ^{- 8}}{4 81 x ^{- 5} y ^{6}}$

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Klaim

D. Nuryani

Master Teacher

Mahasiswa/Alumni Universitas Padjadjaran

Jawaban terverifikasi

Jawaban

, , dan .

Error converting from MathML to accessible text.

, dan

Pembahasan

Ingatlah, untuk sembarang bilangan dengan , berlaku: dengan . Ingat juga, sifat-sifat bilangan berpangkat berikut. Berdasarkan hal-hal di atas, maka: h) i) j) Dengan demikian, , , dan .

Ingatlah, untuk sembarang bilangan dengan a not equal to 0 , berlaku:

n-th root of a to the power of m end root equals a to the power of m over n end exponent

dengan n not equal to 0 .

Ingat juga, sifat-sifat bilangan berpangkat berikut.

Berdasarkan hal-hal di atas, maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cube root of x squared end root over denominator fourth root of 16 y to the power of 6 end root end fraction end cell equals cell x to the power of begin display style 2 over 3 end style end exponent over open parentheses 16 y to the power of 6 close parentheses to the power of begin display style 1 fourth end style end exponent end cell row blank equals cell fraction numerator x to the power of begin display style 2 over 3 end style end exponent over denominator 16 to the power of begin display style 1 fourth end style end exponent times y to the power of 6 cross times begin display style 1 fourth end style end exponent end fraction end cell row blank equals cell fraction numerator x to the power of begin display style 2 over 3 end style end exponent over denominator open parentheses 2 to the power of 4 close parentheses to the power of begin display style 1 fourth end style end exponent times y to the power of 6 cross times begin display style 1 fourth end style end exponent end fraction end cell row blank equals cell fraction numerator x to the power of begin display style 2 over 3 end style end exponent over denominator 2 to the power of up diagonal strike 4 cross times begin display style fraction numerator 1 over denominator up diagonal strike 4 end fraction end style end exponent times y to the power of 6 cross times begin display style 1 fourth end style end exponent end fraction end cell row blank equals cell fraction numerator x to the power of begin display style 2 over 3 end style end exponent over denominator 2 y to the power of begin display style 6 over 4 end style end exponent end fraction end cell row blank equals cell fraction numerator x to the power of begin display style 2 over 3 end style end exponent over denominator 2 y to the power of begin display style 3 over 2 end style end exponent end fraction end cell row blank equals cell 2 to the power of negative 1 end exponent x to the power of 2 over 3 end exponent y to the power of negative 3 over 2 end exponent end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of x to the power of negative 5 end exponent end root over denominator cube root of negative 64 x to the power of negative 6 end exponent end root end fraction end cell equals cell x to the power of negative begin display style 5 over 2 end style end exponent over open parentheses negative 64 x to the power of negative 6 end exponent close parentheses to the power of begin display style 1 third end style end exponent end cell row blank equals cell fraction numerator x to the power of negative 5 over 2 end exponent over denominator open parentheses negative 64 close parentheses to the power of begin display style 1 third end style end exponent times open parentheses x to the power of negative 6 end exponent close parentheses to the power of begin display style 1 third end style end exponent end fraction end cell row blank equals cell fraction numerator x to the power of negative 5 over 2 end exponent over denominator open parentheses negative 2 to the power of 6 close parentheses to the power of begin display style 1 third end style end exponent times open parentheses x to the power of negative 6 end exponent close parentheses to the power of 1 third end exponent end fraction end cell row blank equals cell fraction numerator x to the power of negative 5 over 2 end exponent over denominator negative 2 to the power of 6 cross times begin display style 1 third end style end exponent times x to the power of negative 6 cross times begin display style 1 third end style end exponent end fraction end cell row blank equals cell fraction numerator x to the power of negative 5 over 2 end exponent over denominator negative 2 squared times x to the power of negative 2 end exponent end fraction end cell row blank equals cell negative 2 to the power of negative 2 end exponent x to the power of negative 5 over 2 minus open parentheses negative 2 close parentheses end exponent end cell row blank equals cell negative 2 to the power of negative 2 end exponent x to the power of fraction numerator negative 5 plus 4 over denominator 2 end fraction end exponent end cell row blank equals cell negative 2 to the power of negative 2 end exponent x to the power of negative 1 half end exponent end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator cube root of x to the power of negative 8 end exponent end root over denominator fourth root of 81 x to the power of negative 5 end exponent y to the power of 6 end root end fraction end cell equals cell x to the power of negative begin display style 8 over 3 end style end exponent over open parentheses 81 x to the power of negative 5 end exponent y to the power of 6 close parentheses to the power of begin display style 1 fourth end style end exponent end cell row blank equals cell fraction numerator x to the power of negative begin display style 8 over 3 end style end exponent over denominator open parentheses 3 to the power of 4 close parentheses to the power of begin display style 1 fourth end style end exponent times open parentheses x to the power of negative 5 end exponent close parentheses to the power of begin display style 1 fourth end style end exponent times open parentheses y to the power of 6 close parentheses to the power of begin display style 1 fourth end style end exponent end fraction end cell row blank equals cell fraction numerator x to the power of negative begin display style 8 over 3 end style end exponent over denominator 3 to the power of 4 cross times begin display style 1 fourth end style end exponent times x to the power of negative 5 cross times begin display style 1 fourth end style end exponent times y to the power of 6 cross times begin display style 1 fourth end style end exponent end fraction end cell row blank equals cell fraction numerator x to the power of negative begin display style 8 over 3 end style end exponent over denominator 3 times x to the power of begin display style negative 5 over 4 end style end exponent times y to the power of begin display style 6 over 4 end style end exponent end fraction end cell row blank equals cell 3 to the power of negative 1 end exponent x to the power of negative 8 over 3 minus open parentheses negative 5 over 4 close parentheses end exponent y to the power of negative 6 over 4 end exponent end cell row blank equals cell 3 to the power of negative 1 end exponent x to the power of fraction numerator negative 32 plus 15 over denominator 12 end fraction end exponent y to the power of negative 3 over 2 end exponent end cell row blank equals cell 3 to the power of negative 1 end exponent x to the power of negative 17 over 12 end exponent y to the power of negative 3 over 2 end exponent end cell end table$

Dengan demikian, Error converting from MathML to accessible text. , , dan .

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