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Nilai  untuk  adalah ....

Pertanyaan

Nilai open parentheses x plus 1 close parentheses to the power of 2 over 5 end exponent untuk x equals 4 square root of 2 minus 1 adalah ....

  1. 1 

  2. 2 

  3. 3 

  4. 4 

  5. 5 

Pembahasan Soal:

Jika diberikan bilangan riil a dan bilangan rasional p space dan space q maka berlaku sifat berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell a to the power of p over q end exponent end cell equals cell q-th root of a to the power of p end root end cell row cell a to the power of p times a to the power of q end cell equals cell a to the power of p plus q end exponent end cell row cell open parentheses a to the power of p close parentheses to the power of q end cell equals cell a to the power of p q end exponent end cell end table

Sehingga dapat ditentukan: 

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses x plus 1 close parentheses to the power of 2 over 5 end exponent end cell equals cell open parentheses 4 square root of 2 minus 1 plus 1 close parentheses to the power of 2 over 5 end exponent end cell row blank equals cell open parentheses 4 square root of 2 close parentheses to the power of 2 over 5 end exponent end cell row blank equals cell open parentheses 2 squared times 2 to the power of 1 half end exponent close parentheses to the power of 2 over 5 end exponent end cell row blank equals cell open parentheses 2 to the power of 2 plus 1 half end exponent close parentheses to the power of 2 over 5 end exponent end cell row blank equals cell open parentheses 2 to the power of 5 over 2 end exponent close parentheses to the power of 2 over 5 end exponent end cell row blank equals 2 end table  

Jadi, untuk x equals 4 square root of 2 minus 1 diperoleh nilai dari Error converting from MathML to accessible text..

Jadi, jawaban yang benar adalah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

P. Afrisno

Mahasiswa/Alumni Universitas Sebelas Maret

Terakhir diupdate 11 Juli 2021

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Pertanyaan yang serupa

Hasil dari  adalah ...

Pembahasan Soal:

Ingat sifat bilangan berpangkat berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight a to the power of straight m cross times straight a to the power of straight n end cell equals cell straight a to the power of straight m plus straight n end exponent space dan space open parentheses straight a to the power of straight m close parentheses to the power of straight n equals straight a to the power of straight m cross times straight n end exponent end cell end table

Berdasarkan sifat bilangan tersebut maka penyelesaiannya adalah sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell 243 to the power of 1 half end exponent cross times 3 to the power of 1 half end exponent end cell equals cell open parentheses 3 to the power of 5 close parentheses to the power of 1 half end exponent cross times 3 to the power of 1 half end exponent end cell row blank equals cell 3 to the power of 5 over 2 end exponent cross times 3 to the power of 1 half end exponent end cell row blank equals cell 3 to the power of 6 over 2 end exponent end cell row blank equals cell 3 cubed end cell row blank equals 27 end table 


Dengan demikian, hasil dari 243 to the power of 1 half end exponent cross times 3 to the power of 1 half end exponent adalah 27.

Roboguru

Tentukan bentuk sederhana dari : b.

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis 2 p cubed q to the power of 5 right parenthesis squared cross times 6 p to the power of negative 3 end exponent q squared end cell equals cell 2 squared p to the power of 6 q to the power of 10 cross times 6 p to the power of negative 3 end exponent q squared end cell row blank equals cell 2 squared cross times 6 cross times p to the power of 6 minus 3 end exponent cross times q to the power of 10 plus 2 end exponent end cell row blank equals cell 24 p cubed q to the power of 12 end cell end table

 

Jadi, bentuk sederhana dari left parenthesis 2 p cubed q to the power of 5 right parenthesis squared cross times 6 p to the power of negative 3 end exponent q to the power of 2 end exponent adalah 24 p cubed q to the power of 12.

Roboguru

Bentuk sederhana dari  adalah ...

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 2 cubed close parentheses to the power of 4 times open parentheses 2 cubed close parentheses to the power of negative 5 end exponent end cell equals cell open parentheses 2 cubed close parentheses to the power of 4 minus 5 end exponent end cell row blank equals cell open parentheses 2 cubed close parentheses to the power of negative 1 end exponent end cell row blank equals cell 2 to the power of 3 open parentheses negative 1 close parentheses end exponent end cell row blank equals cell 2 to the power of negative 3 end exponent end cell row blank equals cell 1 over 2 cubed end cell row blank equals cell 1 over 8 end cell end table 

Jadi, Bentuk sederhana dari open parentheses 2 cubed close parentheses to the power of 4 cross times open parentheses 2 cubed close parentheses to the power of negative 5 end exponent adalah 1 over 8.

Dengan demikian, jawaban yang tepat adalah E.

Roboguru

Pembahasan Soal:

Perlu diingat sifat bilangan berpangkat yaitu:

open parentheses a over b close parentheses to the power of n equals a to the power of n over b to the power of n a to the power of negative n end exponent equals 1 over a to the power of n space a t a u space a to the power of n equals 1 over a to the power of negative n end exponent 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 

Dengan menggunakan sifat di atas, hasil dari open parentheses 1 half close parentheses to the power of negative 3 end exponent cross times 2 cubed dapat ditentukan seperti berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses 1 half close parentheses to the power of negative 3 end exponent cross times 2 cubed end cell equals cell 1 to the power of negative 3 end exponent over 2 to the power of negative 3 end exponent cross times 2 cubed end cell row blank equals cell 1 to the power of negative 3 end exponent over 1 cross times 1 over 2 to the power of negative 3 end exponent cross times 2 cubed end cell row blank equals cell 1 over 1 cubed cross times 2 cubed cross times 2 cubed end cell row blank equals cell fraction numerator 1 cross times 2 cubed cross times 2 cubed over denominator 1 cubed end fraction end cell row blank equals cell 2 to the power of 3 plus 3 end exponent over 1 end cell row blank equals cell 2 to the power of 6 end cell end table 

Sehingga hasil dari open parentheses 1 half close parentheses to the power of negative 3 end exponent cross times 2 cubed adalah begin mathsize 14px style 2 to the power of 6 end style.

Jadi, jawaban yang tepat adalah D.

Roboguru

Sederhanakan operasi bilangan berpangkat berikut! a. b.

Pembahasan Soal:

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 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 left parenthesis iv right parenthesis space open parentheses a to the power of m close parentheses to the power of n equals a to the power of m cross times n end exponent  

Berdasarkan sifat-sifat di atas, maka:

a)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a to the power of 3 over 4 end exponent cross times a to the power of negative 3 over 8 end exponent divided by a to the power of 1 over 6 end exponent close parentheses to the power of 8 end cell equals cell open parentheses a to the power of 3 over 4 plus open parentheses negative 3 over 8 close parentheses minus 1 over 6 end exponent close parentheses to the power of 8 end cell row blank equals cell open parentheses a to the power of fraction numerator 18 minus 9 minus 4 over denominator 24 end fraction end exponent close parentheses to the power of 8 end cell row blank equals cell open parentheses a to the power of 5 over 24 end exponent close parentheses to the power of 8 end cell row blank equals cell a to the power of 5 over 24 cross times 8 end exponent end cell row blank equals cell a to the power of 40 over 24 end exponent end cell row blank equals cell a to the power of 5 over 3 end exponent end cell end table

b)

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a to the power of 1 half end exponent cross times a to the power of negative 2 over 3 end exponent divided by b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent end cell equals cell open parentheses a to the power of 1 half plus open parentheses negative 2 over 3 close parentheses end exponent divided by b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent end cell row blank equals cell open parentheses a to the power of fraction numerator 3 minus 4 over denominator 6 end fraction end exponent divided by b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent end cell row blank equals cell open parentheses a to the power of negative 1 over 6 end exponent divided by b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent end cell row blank equals cell open parentheses a to the power of negative 1 over 6 end exponent close parentheses to the power of negative 6 end exponent divided by open parentheses b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent end cell row blank equals cell a to the power of negative fraction numerator 1 over denominator up diagonal strike 6 end fraction cross times open parentheses negative up diagonal strike 6 close parentheses end exponent divided by b to the power of fraction numerator 1 over denominator up diagonal strike 6 end fraction cross times open parentheses negative up diagonal strike 6 close parentheses end exponent end cell row blank equals cell a divided by b to the power of negative 1 end exponent end cell row blank equals cell a divided by 1 over b end cell row blank equals cell a b end cell end table

Dengan demikian, bentuk sederhana dari  open parentheses a to the power of 3 over 4 end exponent cross times a to the power of negative 3 over 8 end exponent divided by a to the power of 1 over 6 end exponent close parentheses to the power of 8 equals a to the power of 5 over 3 end exponent, dan open parentheses a to the power of 1 half end exponent cross times a to the power of negative 2 over 3 end exponent divided by b to the power of 1 over 6 end exponent close parentheses to the power of negative 6 end exponent equals a b.

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