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Pertanyaan

Hasil dari 4 to the power of 1 half end exponent minus 9 to the power of 3 over 2 end exponent plus 8 to the power of 1 third end exponent adalah ...

Pembahasan Video:

Pembahasan Soal:

Perlu diingat konsep dari bilangan berpangkat dengan pangkat berupa pecahan yaitu k to the power of a over b end exponent equals b-th root of k to the power of a end root. Sehingga akan didapatkan

table attributes columnalign right center left columnspacing 0px end attributes row cell 4 to the power of 1 half end exponent minus 9 to the power of 3 over 2 end exponent plus 8 to the power of 1 third end exponent end cell equals cell square root of 4 to the power of 1 end root minus square root of 9 cubed end root plus cube root of 8 to the power of 1 end root end cell row blank equals cell square root of 4 minus square root of 729 plus cube root of 8 end cell row blank equals cell 2 minus 27 plus 2 end cell row blank equals cell negative 23 end cell end table

Jadi, dapat disimpulkan bahwa hasil dari 4 to the power of 1 half end exponent minus 9 to the power of 3 over 2 end exponent plus 8 to the power of 1 third end exponent adalah negative 23.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

N. Puspita

Terakhir diupdate 13 September 2021

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Hasil

Pembahasan Soal:

Ingat sifat-sifat bentuk akar!

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

Maka, perhitungannya yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 9.216 end root minus cube root of 46.656 end root divided by square root of 36 end cell equals cell square root of 96 squared end root minus cube root of 36 cubed end root divided by square root of 6 squared end root end cell row blank equals cell 96 minus 36 divided by 6 end cell row blank equals cell 96 minus left parenthesis 36 divided by 6 right parenthesis end cell row blank equals cell 96 minus 6 end cell row blank equals 90 end table 

Oleh karena itu, jawaban yang benar adalah B.

0

Roboguru

Tentukan hasil akar-akar bilangan berikut! a. b. c.

Pembahasan Soal:

Ingatlah, jika hasil pemangkatan a to the power of n equals b, maka nilai n-th root of b equals n-th root of a to the power of n end root equals a.

Berdasarkan hal tersebut, maka:

a)

table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of negative 729 end root end cell equals cell cube root of open parentheses negative 9 close parentheses cubed end root end cell row blank equals cell negative 9 end cell end table  

b)

table attributes columnalign right center left columnspacing 0px end attributes row cell negative cube root of 64 a to the power of 6 end root end cell equals cell negative cube root of left parenthesis 4 a squared right parenthesis cubed end root end cell row blank equals cell negative 4 a squared end cell end table

c)

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 2 to the power of 10 end root plus cube root of negative 4 to the power of 6 end root end cell equals cell square root of open parentheses 2 to the power of 5 close parentheses squared end root plus cube root of negative open parentheses 4 squared close parentheses cubed end root end cell row blank equals cell 2 to the power of 5 plus open square brackets negative open parentheses 4 squared close parentheses close square brackets end cell row blank equals cell 32 plus open parentheses negative 16 close parentheses end cell row blank equals cell 32 minus 16 end cell row blank equals 16 end table

Dengan demikian, hasil dari cube root of negative 729 end root equals negative 9, Error converting from MathML to accessible text., dan square root of 2 to the power of 10 end root plus cube root of negative 4 to the power of 6 end root equals 16.

0

Roboguru

Tentukan hasil akar-akar bilangan berikut ! a. b. c.

Pembahasan Soal:

Ingatlah, jika hasil pemangkatan a to the power of n equals b, maka nilai n-th root of b equals n-th root of a to the power of n end root equals a.

Berdasarkan hal tersebut, maka:

a)

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 289 end cell equals cell square root of 17 squared end root end cell row blank equals 17 end table  

b)

table attributes columnalign right center left columnspacing 0px end attributes row cell negative square root of 676 end cell equals cell negative square root of 26 squared end root end cell row blank equals cell negative 26 end cell end table

c)

table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of 512 end cell equals cell cube root of 8 cubed end root end cell row blank equals 8 end table

Dengan demikian, hasil dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 289 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 17 end table, negative square root of 676 equals negative 26, dan cube root of 512 equals 8.

1

Roboguru

Tentukan hasil akar-akar bilangan berikut ! g. h.

Pembahasan Soal:

Ingatlah, jika hasil pemangkatan a to the power of n equals b, maka nilai n-th root of b equals n-th root of a to the power of n end root equals a.

Berdasarkan hal tersebut, maka:

g)

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 324 plus cube root of 1.331 end root end cell equals cell square root of 18 squared end root plus cube root of 11 cubed end root end cell row blank equals cell 18 plus 11 end cell row blank equals 29 end table 

h)

table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of negative 216 end root plus fourth root of 1.296 end root end cell equals cell cube root of open parentheses negative 6 close parentheses cubed end root plus fourth root of 6 to the power of 4 end root end cell row blank equals cell negative 6 plus 6 end cell row blank equals 0 end table

Dengan demikian, hasil dari square root of 324 plus cube root of 1.331 end root equals 29, dan cube root of negative 216 end root plus fourth root of 1.296 end root equals 0.

0

Roboguru

Tentukan hasil akar-akar bilangan berikut ! d. e. f.

Pembahasan Soal:

Ingatlah, jika hasil pemangkatan a to the power of n equals b, maka nilai n-th root of b equals n-th root of a to the power of n end root equals a.

Berdasarkan hal tersebut, maka:

d)

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 5 to the power of 4 end root plus cube root of 4 to the power of 6 end root end cell equals cell square root of open parentheses 5 squared close parentheses squared end root plus cube root of open parentheses 4 squared close parentheses cubed end root end cell row blank equals cell 5 squared plus 4 squared end cell row blank equals cell 25 plus 16 end cell row blank equals 41 end table

e)

table attributes columnalign right center left columnspacing 0px end attributes row cell square root of 9 cubed end root minus cube root of 27 squared end root end cell equals cell square root of open parentheses 3 squared close parentheses cubed end root minus cube root of open parentheses 3 cubed close parentheses squared end root end cell row blank equals cell square root of open parentheses 3 cubed close parentheses squared end root minus cube root of open parentheses 3 squared close parentheses cubed end root end cell row blank equals cell 3 cubed minus 3 squared end cell row blank equals cell 27 minus 9 end cell row blank equals 18 end table

f)

table attributes columnalign right center left columnspacing 0px end attributes row cell cube root of 8 squared end root plus cube root of negative 125 to the power of 4 end root end cell equals cell cube root of open parentheses 2 cubed close parentheses squared end root plus cube root of open parentheses negative 5 cubed close parentheses to the power of 4 end root end cell row blank equals cell cube root of open parentheses 2 squared close parentheses cubed end root plus cube root of open parentheses open parentheses negative 5 close parentheses to the power of 4 close parentheses cubed end root end cell row blank equals cell 2 squared plus open parentheses negative 5 close parentheses to the power of 4 end cell row blank equals cell 4 plus 625 end cell row blank equals 629 end table

Dengan demikian, hasil dari square root of 5 to the power of 4 end root plus cube root of 4 to the power of 6 end root equals 41, square root of 9 cubed end root minus cube root of 27 squared end root equals 18, dan cube root of 8 squared end root plus cube root of negative 125 to the power of 4 end root equals 629.

1

Roboguru

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