Roboguru

Bentuk  ekivalen dengan ....

Pertanyaan

Bentuk 9 square root of 3 to the power of x minus 3 end exponent end root square root of 3 to the power of x plus 5 end exponent end root ekivalen dengan ....

  1. 3 to the power of 2 x minus 1 end exponent 

  2. 3 to the power of x minus 1 end exponent 

  3. 3 to the power of x plus 3 end exponent 

  4. 3 to the power of 2 x plus 3 end exponent 

  5. 3 to the power of x plus 1 end exponent 

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 end table

Sehingga dapat ditentukan bentuk ekivalen dari 9 square root of 3 to the power of x minus 3 end exponent end root square root of 3 to the power of x plus 5 end exponent end root sebagai berikut. 

table attributes columnalign right center left columnspacing 0px end attributes row cell 9 square root of 3 to the power of x minus 3 end exponent end root square root of 3 to the power of x plus 5 end exponent end root end cell equals cell 3 squared times 3 to the power of fraction numerator x minus 3 over denominator 2 end fraction end exponent times 3 to the power of fraction numerator x plus 5 over denominator 2 end fraction end exponent end cell row blank equals cell 3 to the power of 2 plus fraction numerator x minus 3 over denominator 2 end fraction plus fraction numerator x plus 5 over denominator 2 end fraction end exponent end cell row blank equals cell 3 to the power of fraction numerator 4 plus x minus 3 plus x plus 5 over denominator 2 end fraction end exponent end cell row blank equals cell 3 to the power of fraction numerator 2 x plus 6 over denominator 2 end fraction end exponent end cell row blank equals cell 3 to the power of x plus 3 end exponent end cell end table     

Jadi, bentuk 9 square root of 3 to the power of x minus 3 end exponent end root square root of 3 to the power of x plus 5 end exponent end root ekivalen dengan 3 to the power of x plus 3 end exponent.

Jadi, jawaban yang benar adalah C.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

P. Afrisno

Mahasiswa/Alumni Universitas Sebelas Maret

Terakhir diupdate 11 Juli 2021

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Pembahasan Soal:

Berdasarkan sifat bilangan berpangkat yaitu a to the power of negative n end exponent equals 1 over a to the power of n comma space a not equal to 0 maka d to the power of negative 1 5 over 8 end exponent diperoleh sebagai berikut.

d to the power of negative 1 5 over 8 end exponent equals 1 over d to the power of 1 begin display style 5 over 8 end style end exponent

Pecahan campuran 1 5 over 8 senilai dengan 1 5 over 8 equals 1 plus 5 over 8 sehingga berdasarkan sifat bilangan berpangkat 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 sehingga diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell d to the power of negative 1 5 over 8 end exponent end cell equals cell 1 over d to the power of 1 begin display style 5 over 8 end style end exponent end cell row blank equals cell 1 over d to the power of 1 plus begin display style 5 over 8 end style end exponent end cell row blank equals cell fraction numerator 1 over denominator d to the power of 1 cross times d to the power of begin display style 5 over 8 end style end exponent end fraction end cell end table

Berdasarkan sifat bilangan berpangkat pecahan yaitu a to the power of m over n end exponent equals n-th root of a to the power of m end root comma space a not equal to 0 dan a to the power of 1 equals amaka

table attributes columnalign right center left columnspacing 0px end attributes row cell d to the power of negative 1 5 over 8 end exponent end cell equals cell 1 over d to the power of 1 begin display style 5 over 8 end style end exponent end cell row blank equals cell 1 over d to the power of 1 plus begin display style 5 over 8 end style end exponent end cell row blank equals cell fraction numerator 1 over denominator d to the power of 1 cross times d to the power of begin display style 5 over 8 end style end exponent end fraction end cell row blank equals cell fraction numerator 1 over denominator d cross times root index 8 of d to the power of 5 end root end fraction end cell row blank equals cell fraction numerator 1 over denominator d root index 8 of d to the power of 5 end root end fraction end cell end table

Jadi d to the power of negative 1 5 over 8 end exponent dinyatakan dalam bentuk akar menjadi fraction numerator 1 over denominator d root index 8 of d to the power of 5 end root end fraction.

Oleh karena itu, jawaban yang benar adalah A.

0

Roboguru

Sederhanakan operasi bilangan berpangkat berikut ! c. d.

Pembahasan Soal:

Ingatlah sifat-sifat bilangan berpangkat 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 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 iii 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 iv right parenthesis space a to the power of negative m end exponent equals 1 over a to the power of m space space    

Berdasarkan sifat-sifat di atas, maka:

c)

table attributes columnalign right center left columnspacing 0px end attributes row cell 3 a to the power of 3 over 4 end exponent cross times 2 a to the power of negative 3 over 8 end exponent cross times open parentheses b to the power of 1 half end exponent divided by b to the power of negative 3 over 4 end exponent close parentheses end cell equals cell 6 a to the power of 3 over 4 plus open parentheses negative 3 over 8 close parentheses end exponent cross times open parentheses b to the power of 1 half minus open parentheses negative 3 over 4 close parentheses end exponent close parentheses end cell row blank equals cell 6 a to the power of fraction numerator 6 minus 3 over denominator 8 end fraction end exponent cross times open parentheses b to the power of fraction numerator 2 plus 3 over denominator 4 end fraction end exponent close parentheses end cell row blank equals cell 6 a to the power of 3 over 8 end exponent cross times b to the power of 5 over 4 end exponent end cell row blank equals cell 6 space root index 8 of a cubed end root cross times b cross times b to the power of 1 fourth end exponent end cell row blank equals cell 6 b space root index 8 of a cubed end root space fourth root of b end cell end table

d)

table attributes columnalign right center left columnspacing 0px end attributes row cell x to the power of negative 5 over 4 end exponent space cross times space x to the power of negative 5 over 8 end exponent space cross times space open parentheses space y to the power of 3 over 4 end exponent divided by y to the power of negative 1 half end exponent close parentheses end cell equals cell x to the power of negative 5 over 4 plus open parentheses negative 5 over 8 close parentheses end exponent cross times open parentheses y to the power of 3 over 4 minus open parentheses negative 1 half close parentheses end exponent close parentheses end cell row blank equals cell x to the power of fraction numerator negative 10 minus 5 over denominator 8 end fraction end exponent space cross times space y to the power of fraction numerator 3 plus 2 over denominator 4 end fraction end exponent space end cell row blank equals cell x to the power of negative 15 over 8 end exponent space cross times space y to the power of 5 over 4 end exponent end cell row blank equals cell y to the power of begin display style 5 over 4 end style end exponent over x to the power of begin display style 15 over 8 end style end exponent end cell row blank equals cell fraction numerator y times y to the power of begin display style 1 fourth end style end exponent over denominator x times x to the power of begin display style 7 over 8 end style end exponent end fraction end cell row blank equals cell fraction numerator y space fourth root of y over denominator x space root index 8 of x to the power of 7 end root end fraction end cell end table

Dengan demikian, hasil dari  3 a to the power of 3 over 4 end exponent cross times 2 a to the power of negative 3 over 8 end exponent cross times open parentheses b to the power of 1 half end exponent divided by b to the power of negative 3 over 4 end exponent close parentheses equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank b end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell root index 8 of a cubed end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fourth root of b end cell end table, dan x to the power of negative 5 over 4 end exponent space cross times space x to the power of negative 5 over 8 end exponent space cross times space open parentheses space y to the power of 3 over 4 end exponent divided by y to the power of negative 1 half end exponent close parentheses equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator y space fourth root of y over denominator x space root index 8 of x to the power of 7 end root end fraction end cell end table.

0

Roboguru

Tentukan hasil pemangkatan bilangan berpangkat berikut ! a. b. c.

Pembahasan Soal:

Ingatlah sifat-sifat bilangan berpangkat 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 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 iii right parenthesis space a to the power of negative m end exponent equals 1 over a to the power of m    

Berdasarkan sifat-sifat di atas, maka:

a)

table attributes columnalign right center left columnspacing 0px end attributes row cell 8 to the power of 2 over 9 end exponent cross times 8 to the power of 4 over 9 end exponent end cell equals cell 8 to the power of 2 over 9 plus 4 over 9 end exponent end cell row blank equals cell 8 to the power of 6 over 9 end exponent end cell row blank equals cell 8 to the power of 2 over 3 end exponent end cell row blank equals cell cube root of 8 squared end root end cell row blank equals cell cube root of 64 end cell row blank equals cell cube root of 4 cubed end root end cell row blank equals 4 end table

b)

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

c)

table attributes columnalign right center left columnspacing 0px end attributes row cell 9 to the power of 3 over 4 end exponent cross times 9 to the power of 6 over 8 end exponent end cell equals cell 9 to the power of 3 over 4 plus 6 over 8 end exponent end cell row blank equals cell 9 to the power of fraction numerator 6 plus 6 over denominator 8 end fraction end exponent end cell row blank equals cell 9 to the power of 12 over 8 end exponent end cell row blank equals cell 9 to the power of 3 over 2 end exponent end cell row blank equals cell square root of 9 cubed end root end cell row blank equals cell square root of 729 end cell row blank equals 27 end table

Dengan demikian, hasil dari  8 to the power of 2 over 9 end exponent cross times 8 to the power of 4 over 9 end exponent equals 4, 4 to the power of 1 half end exponent cross times 4 to the power of negative 1 end exponent equals 1 half, dan 9 to the power of 3 over 4 end exponent cross times 9 to the power of 6 over 8 end exponent equals 27.

0

Roboguru

Hasil pemangkatan dari

Pembahasan Soal:

Berdasarkan sifat bilangan berpangkat yaitu 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 maka open parentheses a to the power of 9 over 4 end exponent divided by a to the power of 3 over 4 end exponent close parentheses to the power of negative 5 end exponent diperoleh sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a to the power of 9 over 4 end exponent divided by a to the power of 3 over 4 end exponent close parentheses to the power of negative 5 end exponent end cell equals cell open parentheses a to the power of 9 over 4 minus 3 over 4 end exponent close parentheses to the power of negative 5 end exponent end cell row blank equals cell open parentheses a to the power of 6 over 4 end exponent close parentheses to the power of negative 5 end exponent end cell end table

Berdasarkan sifat bilangan berpangkat 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 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a to the power of 9 over 4 end exponent divided by a to the power of 3 over 4 end exponent close parentheses to the power of negative 5 end exponent end cell equals cell open parentheses a to the power of 6 over 4 end exponent close parentheses to the power of negative 5 end exponent end cell row blank equals cell a to the power of 6 over 4 cross times negative 5 end exponent end cell row blank equals cell a to the power of negative 30 over 4 end exponent end cell end table

Berdasarkan sifat bilangan berpangkat a to the power of negative n end exponent equals 1 over a to the power of n comma space a not equal to 0 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a to the power of 9 over 4 end exponent divided by a to the power of 3 over 4 end exponent close parentheses to the power of negative 5 end exponent end cell equals cell a to the power of negative 30 over 4 end exponent end cell row blank equals cell 1 over a to the power of begin display style 30 over 4 end style end exponent end cell row blank equals cell 1 over a to the power of begin display style fraction numerator 28 plus 2 over denominator 4 end fraction end style end exponent end cell row blank equals cell 1 over a to the power of begin display style 28 over 4 end style plus begin display style 2 over 4 end style end exponent end cell row blank equals cell 1 over a to the power of 7 plus begin display style 2 over 4 end style end exponent end cell end table

Berdasarkan sifat bilangan berpangkat 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 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a to the power of 9 over 4 end exponent divided by a to the power of 3 over 4 end exponent close parentheses to the power of negative 5 end exponent end cell equals cell 1 over a to the power of 7 plus begin display style 2 over 4 end style end exponent end cell row blank equals cell fraction numerator 1 over denominator a to the power of 7 cross times a to the power of begin display style 2 over 4 end style end exponent end fraction end cell end table

Berdasarkan sifat bilangan berpangkat pecahan yaitu a to the power of m over n end exponent equals n-th root of a to the power of m end root comma space a not equal to 0 maka

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses a to the power of 9 over 4 end exponent divided by a to the power of 3 over 4 end exponent close parentheses to the power of negative 5 end exponent end cell equals cell fraction numerator 1 over denominator a to the power of 7 cross times a to the power of begin display style 2 over 4 end style end exponent end fraction end cell row blank equals cell fraction numerator 1 over denominator a to the power of 7 cross times fourth root of a squared end root end fraction end cell end table

Jadi hasil pemangkatan dari open parentheses a to the power of 9 over 4 end exponent divided by a to the power of 3 over 4 end exponent close parentheses to the power of negative 5 end exponent adalah fraction numerator 1 over denominator a to the power of 7 space fourth root of a squared end root end fraction.

Oleh karena itu, jawaban yang benar adalah A.

9

Roboguru

Tentukan hasil pemangkatan bilangan-bilangan berikut! 1.

Pembahasan Soal:

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 a to the power of m over n end exponent cross times a to the power of p over q end exponent equals a to the power of m over n plus p over q end exponent

Berdasarkan sifat-sifat di atas, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell 8 to the power of 1 half end exponent cross times 8 to the power of 1 over 6 end exponent end cell equals cell 8 to the power of 1 half plus 1 over 6 end exponent end cell row blank equals cell 8 to the power of 4 over 6 end exponent end cell row blank equals cell 8 to the power of 2 over 3 end exponent end cell row blank equals cell cube root of 8 squared end root end cell row blank equals cell cube root of 64 end cell row blank equals 4 end table

Dengan demikian, hasil dari 8 to the power of 1 half end exponent cross times 8 to the power of 1 over 6 end exponent adalah 4.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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